IDs vs. Classes

IDs and Classes seem almost identical to me.

In fact, it seems that IDs are just Classes that can only be used in the
body once.

Is that true?

Also, the spec explicitly states that a simple selector can have only
1 class (in section 1.4), but I could find no such limit on the number of
IDs per simple selector.

Is that a purposeful omission (and simple selectors can have multiple
IDs) or does the same limit apply to IDs (only 1 per simple selector)?