The bead seat diameter (BSD) is the critical measurement. That's where the bead sits on the rim.
S-2 & S-7 refer to the width and shape of the rim, not any specific diameter. Both come in several diameters.
In general S-2 is balloon, S-7 is middle weight.
in 26" Schwinn 26 x 1 3/4 Middleweight, bsd=571mm
in 26" Schwinn 26 x 2.125 Balloon, bsd=559mm
the difference is too much for any hope of swaping. Even 2 mm can be a royal pain.
26" x 1.75" is not a Schwinn size but is the same bsd as balloon of 559.
Look at this reference chart.
http://www.schwinnbikeforum.com/index.php?topic=24638.0You can also look at the Sheldon Brown page on rim sizes.
http://sheldonbrown.com/tire-sizing.htmlneither of these references are 100% complete.
Wire bead tires don't stretch much.
Walmart tires that come in a box, stretch like crazy. Those sure are not your racer kevlar beads in there, more like cheap nylon.
For identifying your rims, if they are stock, see the drawings on the first link above. They came in chrome or painted. Other brands of rims have rather different shapes and usually don't have the knurling. It's plenty common to find the wheels have been changed out on older Schwinns.