SCHWINN had different thoughts about how to size tires, they started making their own "standard" sizes and thought the other manufacturers would follow along ... they didnt. so you end up with s-2, s-7, s-5 & s-6 and maybe a couple others i dont know about. i believe i read that schwinn "invented" the balloon tire 26x2.125 (s-2) so a standard 2.125 tire should work on a schwinn s-2 but i know the s-5, s-6 (both are 1-3/8 tires) and the s-7 (1-3/4) are schwinn specific. the tires will have to say "fits S-7 or S-5/S-6"
there is also a standard 1-3/8 tire size usually found on "english" style bikes, those wont work unless they say "fits S-5 or S-6"
the tires arent usually in stock at most bike shops but theyre not too hard to find for cheap.
also schwinn rims are doublewalled, alot stronger than most of the standard cheapo rims bikes come with today when it comes to curb hits and flexing.