These are two very similar words with only one letter difference. Clarification is important in order to understand what is the animal and what is the gem.
Ammonite: This is a prehistoric sea squid that existed anywhere between 400 - 66 million years ago. Their fossilized shells can be found all over the world including areas such as Madagascar, Canada, Russia, the UK, etc. In general, these shells often appear colorless (so white, brown or black). Sometimes, the appearance may even remind the viewer of a "mother of pearl". However, there is usually little or no color.
From Left to Right: (1) Ammonite fossil - no color, (2) Ammonite fossil - no color, (3) Ammonite Fossil - mother of pearl, (4) Ammonite fossil - split from Madagascar.
Ammolite: This is the gem grade shell of the ammonite and it can only be found within a small corridor in Southern Alberta. While you can find colored shell within the United States as well as some of the other Prairie Provinces, it is often highly degraded and not considered to be gem grade quality.
From Left to Right: (1) Gem Grade Ammonite Fossil, (2) Close-up of Gem Grade Fossil, (3) Sterling Silver Ammolite Pendant, (4) Imperial free-form pendant
So to sum it up, all ammolite is found on ammonite but not all ammonite contain ammolite.
Let's try it this way...
The image below features an ammonite ... however it is colorless so this is not ammolite.
The image below this one is an ammonite with ammolite on it... this is often referred to as a gem grade ammonite.
As can be observed there is quite a large color difference when referring to an ammonite compared to a gem grade ammonite. And that color is called ammolite.
Hopefully that clears up the confusion!