Part of the problem with wheel sizes is that there are three different systems, and they don't always measure the same thing. In the case of the "700c" and "28" specifications, they also aren't very accurate. For example, "700c" is part of a French measurement system which measures the nominal diameter of the outside of the tire in millimetres, but adds the "A", "B" "C" and "D" which are "narrow", "medium", "wide" and "very wide" but notably they don't really define this. Of course his has two problems, firstly what are "narrow" and "wide" in real numbers? Also, a "wide" tyre will obviously have a bigger diameter than a "narrow" tyre for the same rim size. In theory the second number on the tyre, say "28c" gives the nominal width, but it still isn't very accurate.
With inch sizes it's even worse: the size a "28 inch" tyre is again the nominal outer dimension, So a tyre with "28 x 1.50" when mounted on a wheel, will give a nominal diameter of about 28 inches and a nominal width of 1.5 inches, which gives the same problem as before. On top of this, imperial tyres can look the same size, but not be; for some reason, a tyre with "28 x 1.5" on the outside my not fit the same rim as a "28 x 1/2" tyre.
To add to the confusion of course, a "29 inch" tyre, the new mountain bike standard, fits the same rim size as a 28" tyre, they're just fatter.
Because of this there is now a new and much more accurate system, the ETRTO (European Tyre and Rim Technical Organisation) specification, which is also ISO standard. This ignores the outer diameter and measures the bead size, the point where the tyre hooks onto the rim, so it is far more reliable.
A tyre with "622" as the ETRTO number will fit the same rim as a 28" tyre, and also a "700" tire in the French system. The other number in the ETRTO system is the nominal width, so a tyre with "37-622" is 37mm wide by 622mm bead diameter, "50-622" is the same diameter and 50mm wide etc.
Mercifully, all new tyres are required to have their sizes shown in all three systems, so you can either ignore the imperial and French system, and just use the ETRTO/ISO numbers. You can also look at the sizing on the old tyres and find a new tyre showing that size, then find the ETRTO number on that tyre, and bingo, you know what to look for.