The two things mean something rather different. "Too little, too late" indicates there was two shortfalls, "a little too late" indicates there was one shortfall.
Effort on your homework was too little and too late.
Here the speaker is indicating both that there was too little effort on the homework and that that effort was applied too late.
Effort on your homework was a little too late.
Here the speaker indicates only that the effort was too late, and the lateness was only a little lateness. Nothing is said of the size of the effort, only its tardiness.
The word "race" carries a host of (usually negative) connotations in English as well, and in the wrong situation you can cause a commotion with it. Unfortunately it is the only word we've got that really means what you want.
I'm going to answer this with as little social commentary as possible, but just to be clear, races of humans are not biologically meaningful categories, but ethnicities can be sociologically meaningful.
A race is a distinct group of people, separated from others based on biological factors, usually skin color. It also often corresponds to place of origin or ancestry.
ex: Pacific Islanders or Australian Aborigines are often viewed as belonging to particular races.
An ethnic group or someone's ethnicity is a distinct group of people, separated from others based on sociological or historical factors. It may or may not correspond to race.
ex: Jewish or Hispanic people belong to particular ethnicities, but can be of any race.
If, conversationally, you chose to ask someone about their heritage, it would be safer to ask for their ethnicity than their race, and they would likely give you their race rather than their ethnic group.
However, in your example, worldbuilding, you are defining a group of people by their physical characteristics (and probably also by their social characteristics) so it would be appropriate to call them a race.
ex: In World of Warcraft, the Orcs are a race of green skinned warriors who value bravery in battle.
You would definitely use the word race in this context, as Orcs are a distinct biological population from Trolls or Elves or Humans. It would be trickier if they were all groups of humans who differed only in superficial physical characteristics, but people would be more understanding of the use of race in a completely hypothetical situation like that.
Best Answer
There are a number of terms for sporting events. Unfortunately each can have its own particular term:
The most generic is "game":
This is appropriate for sports like baseball, football/soccer, basketball, and so on.
Tennis, however plays a match, as does boxing and other one-on-one sports/games.
A single boxing (or other fighting sport) match can also be called a bout.
Golfers play a round of golf, but a complete set of rounds, often over a period of days is called a tournament.
Other sports can also have tournaments, especially when each contestant plays against more than one opponent. For example, a table tennis tournament will consist of a series of matches, with players being eliminated until you get to the final match to determine the tournament winner.
Race is appropriate for sports that are contests of speed -- biking, running, horse racing, auto racing, etc.
A collective event which might have many different types of sports all going on at the same time can be called a meet. Sports such as "track and field" or swimming have meets against their opponents, where all the different events go on at the same time, in different areas.
Some sports have their own unique terminology. Cricket, for example, calls their games a Test match or simply a Test (although there are variations with other names).
This is not meant to be a complete list, but it should be enough to get started.