What is Noise Cancelling?
Noise cancelling headphones use microphones to listen to the incoming sound, then some fancy processing creates inverse waves which get fed back into the headphones. These inverse waves cancel out the ambient sound. One way to think about this is if the ambient noise (aeroplane engines / air conditioning, say), is “+1” the headphones would create and add “-1” so your ear hears 0 (i.e. nothing, within reason of course).
What is Noise Isolating
Many in-ear and on-ear headphones isolate you from ambient noise. Some are better than others. The idea here is a physical barrier between your ear and the offending sounds.
With over-ear headphones, the noise isolation usually isn’t a lot, but enough to muffle the surrounding sound somewhat.
With in-ear headphones, how much sound they reduce is based entirely on how good a seal you’re able to get. Everyone’s ears are different, and as such, in-ear headphones fit everyone differently.