As usual, Sheldon's got the answers.
ISO 622 is the unambiguous way of referring to the following rim sizes:
- 700c (you see this marketing on road, hybrids; this is from the French system; the c is often dropped, but there are rare a,b sizes)
- 29"x decimal (you see this on mountain bikes; usually only applied to wide rims)
- 28"x decimal (particularly in Germany)
- 28" x some fractions (seems to be a rare Canadian / northern European thing).
700 mm is roughly 27.5 inches, so if you mounted a reasonable tire on it, you'd get around 28 inches (hence the name 28"). For mountain bikes, you'd get a bigger tire giving an outside diameter of 29"+.
In theory, any tire which can be mounted to a rim marked as any above sizes can be mounted to the others, but in practice you want the rim width to be appropriate to the tire size you're mounting.
In terms of which way you should refer to this wheel size, ISO 622 is unambiguous. If its being used on a road bike or hybrid, 700c is also a good way to refer to it. If its being used on a mountain bike with a big tire, 29" is also a good way to refer to it.