Yes, you will want to look for "Shoyu" in a regular grocery store that will probably be made of fermented soy beans. You could also make the trip out to an Asian grocery store - a simple yet effective way to start an adventure :)
Most American grocery store soy sauce is also not authentic soy sauce. Soy sauce has to be aged from soy, salt, wheat, and a fermentation starter. American grocery store soy sauce is typically salt water with flavor additives.
Ingredients for a cheap American soy sauce: soybean, corn, water, sugar, sodium benzoate, salt, caramel color, monosodium glutamate, citric acid, potassium sorbate.
As a big counterexample, Kikkoman is popular enough in the USA to carry in mainstream grocery stores, and is a legitimate soy sauce. I go to the Korean market here when I can for soy sauce (in which case I often get Sempio 501 or 701), but when I don't have time for a separate trip for some reason, I get Kikkoman from the big-box store and it's perfectly reasonable. The level of salt is still relevant, though.
If you start getting into different kinds of legit soy sauce then you'll find more subtle differences of course, and depending on what you're cooking, they may be relevant. I don't cook at home with enough precision for the difference between “primary” soy sauces to matter much, but if you start learning an actual cuisine, that's different.
I haven't been actually keeping track, but I can't recall a time I was in a store with only one brand of soy sauce and it wasn't Kikkoman. Maybe just because I'm in California though?
Tamari is a good answer to this problem (soy sauce made without wheat). Depending on the brand it has less salt than regular soy sauce and, as it has a richer flavour, you need less of it.