Early occurrences of 'sales pitch' and 'making a pitch' in the 1900s
The person who coined of the phrase "sales pitch" is not evident from early written instances of the phrase that a Google Books search finds. But those search results point to a very likely source for the popularization of the phrase: The Billboard magazine. A Google Books search finds 21 instances of "sales pitch" from 1950 and earlier—and 20 of them are from The Billboard. (The only exception to this pattern is from a 1949 issue of Television Magazine.)
The earliest instances are from 1943. From "Gabbers Sell in New Garb: Ether Salesmen Now Part of Over-All Production; Dough for Performance Not Names" in The Billboard (November 20, 1943):
Smooth and Subtle Selling
The move away from solo announcers on shows is just one phase of a general trend toward subtler and smoother air salesmanship. The sales pitch, instead of interrupting program continuity, is now, an integrated part of the show. It's as much a production as the entertainment itself.
And from "Blues Sales Pitch For Swing Frolics Audience on Job," in The Billboard (December 11, 1943):
The show, billed as the war workers" own amateur hour, is heard in about 350 war plants, according to web salesmen. This is what guarantees, they claim, close to half a million listeners.
Besides the war plant angle the Blue sales' pitch plugs the recent publicity of Swing Shift, including the auditioning of contestants at the Skouras theaters and 20th Century-Fox's short.
The related phrase "making a pitch for X" also appears frequently in The Billboard, too, starting in 1942. From "Sellers of E. T. Programs Report Demand for Shows Point Up Fem Angle; Producers Trim Budgets" in The Billboard (July 4, 1942):
Despite this [downturn in production of transcribed programs, aka "wax programs"], there is plenty of business lying around for those producers of wax shows who are still making a pitch for the business. Competition has become noticeably less keen, and the transcription producers with competent sales organizations are successfully peddling their stuff.
This is among 24 instances of "making a pitch for" that appears in issues of The Billboard from 1950 or earlier. Google Books did not turn up any instance of the phrase "making a pitch for" from a source other than The Billboard until 1957.
Early occurrences of 'making a pitch' and allied formulation in the 1800s
I was quite surprised, however, to find the expression "making a pitch" used in a very similar sense almost a hundred years earlier. From Henry Mayhew, "Of the Street-Sellers of Rings and Sovereigns for Wagers," in London Labour and the London Poor (1851):
"When I came out of prison [for supposedly stealing a string of pots], I went to Epsom races, thinking to get a job there at something or other. A man engaged me to assist him in 'pitching the hunters.' Pitching the hunters is the three sticks a penny, with the snuffboxes stuck upon sticks; if you throw your stick, and they fall out of the hole, you are entitled to what you knock off. I came to London with my master the pitcher-hunter, he went to a swag shop in Kent-street, in the Borough, to purchase a new stock. I saw a man there purchasing rings, this was little Ikey, the Jew; some days afterwards I saw him making a pitch, and selling very fast. I had fourpence in my pocket; went to Kent-street, to the swag shops, bought a dozen rings, and commenced selling them. I sold that day three dozen; that wasn't bad considering that my toggery was very queer, and I looked anything but like one who would be trusted with ten pounds' worth of gold rings."
The story that the ring sellers told prospective buyers was that two sporting noblemen had wagered with one another about whether a person selected at random (the ring seller) can sell a certain quantity of genuine solid-gold rings within a fixed period of time—an hour, say—for a penny apiece. The idea was that one nobleman had bet the other that most Londoners offered the chance to get something valuable for practically nothing (in the "new lamps for old" tradition) would be so suspicious of the bargain that they would turn it down. In reality, of course, there were no sporting noblemen, and the ring seller had bought the rings (which were imitation gold) himself for sevenpence a dozen. The scam sounds sounds absurdly silly until you consider modern email messages from Nigerian oil ministers seeking help from strangers to keep their money safe while they flee the country.
Mayhew's ring-seller informant remarks,
"I make many a pitch, and do not sell a single ring; and the insults I receive used to aggravate me very much, but I do not mind them now, I'm used to it."
Elsewhere in the same book, Mayhew explain the meaning of "make a pitch" in the context of pitching coins in the air:
"Three-up" is played fairly among the coster-mongers; but is most frequently resorted to when strangers are present to "make a pitch,"—which is, in plain words, to cheat any stranger who is rash enough to bet upon them. ... [An] adept illustrated his skill to me by throwing up three halfpennies, and, five times out of six, they fell upon the floor, whether he threw them nearly to the ceiling or merely to his shoulder, all heads or all tails. The halfpence were the proper current coins‚ indeed they were my own; and the result is gained by a peculiar position of the coins on the fingers, and a peculiar jerk in the throwing. There was an amusing manifestation of the pride of art in the way in which my obliging informant displayed his skill.
It thus appears that "making a pitch" in the street scam sense may have originated with the coin pitching of "three-up."
However, Mayhew also cites several street merchants he spoke to as using the term "a pitch" to refer to an outdoor stall in a fixed locality where items such as fruit or meat are sold, and hence to such street businesses themselves. In this case, pitch may have come from the notion of pitching (that is, setting up) the stall prior to the day's work (as we sometimes speak of "pitching a tent" today). And once pitch is associated with stall sellers, it isn't much of a stretch to imagine people linking the sellers' attempts to hawk their wares with the idea of "pitching."
Yet another complication involves use of the phrase "make a pitch" in the sense of a hawk swooping down to attack its prey. From William Bingley, Animal Biography, Or, Authentic Anecdotes of the Lives, Manners, and Economy of the Animal Creation, volume 1 (1803):
There have, however, occurred instances in which the Turkey Cock has not been found wanting in prowess:—a gentleman of New York had brought from a distance a large Turkey-Cock and Hen, and a pair of Bantams, which were given to him by a relation; and he put them into his yard with some other poultry. Some time after, as he was feeding them from the barn-door, a large hawk suddenly turned the corner of the barn and made a pitch at the Bantam hen: she immediately gave the alarm, by a noise which they generally make on such occasions; when the Turkey-cock, who was at the distance of about two yards, and no doubt understood the hawk's intentions, and the imminent danger of his old acquaintance, flew at the hawk with such violence, and gave him so severe a stroke with his spurs, as he was about to seize his prey, as to knock him from the hen to a considerable distance; and the timely aid of this faithful auxiliary completely saved the Bantam from being devoured.
Conclusions
The gap in written instances of "making a pitch" between Henry Mayhew in 1851 and The Billboard magazine in 1942 is puzzling, especially since the notion of crying up one's wares seems to be a common theme of the usage in both instances.
Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013) traces "make a pitch for" to the late 1800s but doesn't acknowledge the absence of written examples of the phrase during the first four decades of the twentieth century:
make a pitch for Say or do something in support of someone or something [example omitted]. This expression originally alluded to inflated sales talk that was "pitched" (in the sense of "thrown") at the listener. {Slang; late 1800s}
J.S. Farmer & W.E. Henley, Slang & Its Analogues, volume 5 (1902) has this entry for pitch:
Pitch, subs. (showmen's and tramps').—(1) A place: of sale or entertainment. Also (2) a performance or sale. Hence TO PITCH (or DO A PITCH) = to do business; ...
[First citation:] 1851–6. MAYHEW, London Lab[our and the London Poor], 1. xii. In consequence of a new Police Regulation 'stands' or PITCHES have been forbidden.
Farmer & Henley identify several additional instances of pitch in these senses from the later 1800s, but most of them seem to have come from UK sources.
Despite considerable searching, I haven't been able to identify a clear and continuous path in the usage of "making a pitch" between London in 1851 and the United States in the early 1940s, though some such connection seems reasonable enough. In any case, during the 1940s in the United States, "sales pitch" and "making a pitch" were used multiple times to describe promotional efforts on behalf of various appeals to potential customers, and the entity responsible for popularizing both phrases was The Billboard magazine.
Best Answer
They mean different things. "Leave nothing out on the pitch", means give everything you have to the game. Never come off the field feeling you could have played harder. "Leave it out on the pitch" means you are rivals in the game, but friends off the field. In rugby you still see at the final whistle the home team running to the side of the pitch to form a tunnel to applaud off the away team, who 30 seconds before they were practically fighting against.