D3MON
Hardcore RCTalk User
i don't race but i recently subscribed to his channel, lots of good information for racing and bashing alike. more or less like he is talking "to" you not "at" you.The S number on Lipo batteries are literally how many cells are inside the wrap/case. So if you ripped one open, you would see a 2s has 2 cells stacked together, a 4s has 4, etc.
Single cells are 3.7v each which is where the total voltage comes from for each S number.
2s is 3.7v x 2 = 7.4v total voltage
3s is 3.7v x 3 = 11.1v total voltage, and so on.
Tracks have a 2s (7.4v) requirement for 10th scale. 1/8th scale has a limit of 4s. Anything else is used for other aspects of the hobby such as bashing or crawling. But for racing specifically you're only dealing with 2s for 1/10 and 4s for 1/8
You can use whatever C rating you like on the batteries you get, the higher generally better, but you also reach a point where the rating is mostly marketing fluff and your esc will still only draw what it needs.
As far as there seeming to be an advantage in spec/stock class racing, there's little advanced tricks you can do as well such as motor timing, esc timing, charging batteries at super high amps to increase discharge rate (which i don't recommend) and things like that. I haven't gotten too in depth with that stuff yet and it's all well past the amateur level of things. Just make sure you get a motor that has a timing feature. it's the easiest way to dial in a car to your track and adjust top end/acceleration without changing all your gearing.
There's some really good youtubers who have great resources on the racing aspect. One of my favs that I would highly recommend is Ryan Harris from the Jconcepts team. He has a lot of informative info and his even coverage is really nice because he talks you through exactly how he's setting up his car, changing his driving style, and preparation at each race, plus he's just a super nice guy it seems. he races 17.4 2wd spec, and 13.5 stadium truck and 4wd at most of the events he attends.
https://www.youtube.com/user/mrxstiles/videos
Here's a good one to watch as it answers your question above directly.