S-7 wheels take 1 3/4" tires which are a different diameter than the 1.75 or 2.125 tires which fit S-2 rims. No way they will interchange. You will find the Schwinn S-7 wheel and tire is larger than a standard rim with a 1.75 tire mounted.
To determine if your frame is a balloon or middleweight, use the first 3 fingers on your hand. Just behind the seat post clamp there is a triangular area formed by the tubes coming up from the rear end and the upper fender bracket. If you insert your 3 fingers into this triangle area, resting them on the fender bracket, you'll be able to tell the difference. On the balloon frame, your fingers will go into the triangle easily with room to spare. On a middleweight, your fingers won't fit...or, they will fit very tight depending on the size of your fingers, of course. I'll take some pics tomorrow of my frames and fingers and post them here so you'll know. B607