Normalize vs Limit

Limiting is a dynamic process.  One feeds a signal in and compresses it, ie. squeezing out the dynamic range values between the loudest and softest levels of the signal.  That should make the signal quieter, so there is usually a make up gain knob.  Limiting is simply an extreme form of compression, usually considered at least 10 to 1 ratio.  
 
Normalizing is an off line process, where the loudest part of a signal is identified and the ENTIRE track volume is then raised so that loud part is still loud, but constrained by whatever the user sets as the loudest signal.  Say your track's loudest moment is -3 dB.  You raise that to -.3 dB, and the rest of the signal is raised by 2.7 dB too.  The dynamic range hasn't been squeezed or compressed, just transposed louder.  Normalizing doesn't raise your average level usually as much as limiting, since quiet sections are still much lower than the loudest.