I have several bikes. One has 700x32c tires. Another has 700x38c. The 700x38c tires are slightly smaller than the 700x32c tires - I mean the circumference of the tire, as if you're putting the tire in your palm and wrapping your fingers around it and touching your fingers and thumb. Know what I mean? I thought 38's would be bigger than 32's. What do I not understand about tire sizing? Thanks!
Actually, the "38c" part really only refers to the width of a tyre. The cross-section profile of a tyre isn't always perfectly round. You can have a wide squat tyre, like the Tioga CitySlickers which are modeled after a motorcycle tyre. It is roughly 1.5 times as wide as it is tall. On the other extreme, you can have narrow-profile time-trial type tyres that are about 0.8 times as wide as they are tall.
Pull out the calipers and measure the actual casing-width. The rubber part doesn't count. May be tough on some tyres due to the knobbies, but you can usually wedge the calipers in between them.