One of the other answers has provided a nice link to the Wikipedia entry for baseball metaphors for sex. There are, as the top comment on this question notes, four bases in baseball, and these have corresponding sex acts associated with them.
The sexual contact associated with each base has evolved dramatically since I was a teenager, although "home base" or "home run" has always meant intercourse, and "first base" has always meant kissing or snogging.
To use the expression correctly, you get or make it to a base, per my comment:
I got to second base with that girl yesterday.
I didn't think I had a chance, but I made it to third base with her last night.
You don't use "hit" with "bases," but you can use the baseball terms that correspond to hits:
I hit a triple when I took her home last night.
means to get to third base. It's double for second base, single for first base.
You can also "score," which is the same as hit a home run or get to home base.
About the House quotation, if I interpret it correctly, they had intravaginal sex twice and then she performed oral sex on him. If we say home base = fourth base, that's 4 + 4 − 3 = 5, the subtraction because he was receiving instead of giving. But this is a joke, and probably not intended to be analyzed too closely.
And here's another handy diagram.
To answer the presenting question first,
No, the two constructions are not always the same in meaning. There are several reasons for this.
The most important one is the point made in the comments, that logic (and computer languages) are not the same as natural language; and, while logical statements can usually be put into English, any English sentence containing quantifiers (especially if it also contains modals or negatives of any kind) is multiply ambiguous.
Logic is a stick-figure representation of linguistic meaning, and like stick figures, it leaves out a lot and expects you to fill it in from your imagination (or presuppositions, to the extent there's any difference). Logic assumes that quantifiers (like all, each, every, some, and most) modify nouns (all the men, each man, etc.)
But in fact quantifiers can "float". Some, but not all, of them can appear in adverbial position, before the main verb or after the first auxiliary verb. This doesn't change the meaning, but it does change the grammar. Especially with negatives.
- All the men read the book. ==> The men all read the book.
- Each man read the book. ==> The men each read the book.
- Every man read the book, but not *The men every read the book.
When there is a negative morpheme in the sentence, the relative order of the negative and the quantifier can produce meaning problems.
- Not all the men read the book. ≠ All the men didn't read the book.
(the first says some didn't read it, but the second is ambiguous)
- The men didn't all read the book. (same as Not all the men...)
The real problem here is that there are rules in logic for order of operators (modals, negative, and quantifiers) in propositions:
(∀x: Man(x)) (Read (x, Book)) is unambiguous, and so is ¬(∀x: Man(x)) (Read (x, Book)), and(∀x: Man(x)) ¬(Read (x, Book))
The first one says for every man, that man read the book. The second says that the first one is not true (for whatever reason) of every man. The third one says that for every man, that man did not read the book. The first and the third are contradictory, and the second one can report multiple situations.
That's logic.
Syntax requires modifiers to have certain positions in the sentence, whatever the math rules of logic require.
Best Answer
What RyeBread said.
"It was many and many a year ago, in a kingdom by the sea" is the opening of a great poem by Edgar Allen Poe. Anabel Lee
Presumably Dick Cavett assumes that anyone over a certain age educated in the US (i.e. those who were viewers of his TV show) read the poem in school, and will understand the reference.