26" tires too big for 26" rim?

So, I've got an old (1987) mtn bike I'm outfitting for touring - with the intent of a 4 day solo tour on the coast in 2.5 weeks. Step 1 was to swap the 1.95" knobblies for 1 3/8" slicks. No problem, right? Got some cheap 26x 1-3/8" tires and tried installing them today. There's no way they'll fit! They look more like 28" tires!! I can hook the bead at one side of the wheel, but at the other side, there's a 1-2" gap!! Both of the new ones are equally large, both are stamped 26", and both are far bigger than the 26x1.95 tires I took off. Is something strange going on here?? Or was there some glitch in making the tires?? Is the shop playing tricks on me?? (And yes, I checked to make sure the rims are not 24").