Yes. In fact, a limiter is a compressor set to extreme settings.
Not quite.
A limiter, as the name implies, limits the audio level. If the level goes above a certain threshold, it is limited - of course this eliminates peaks, how else should it work?
A compressor adjusts the gain on the fly (the sensitivity of the effect depends on the chosen parameters), to make quiet parts louder and loud parts quieter.
The essential difference is that a limiter just does the latter, but not the former. An audio signal can easily "pump" when applying a compressor wrong, and that's most often the cast if you actually wanted to use a limiter but used a compressor instead.