Two words for basically the same thing. I’m definitely guilty of using both terms interchangeably which probably isn’t helpful for someone trying to get their head around cloth nappies.
Both an insert and a booster are there to absorb wee. And that’s really all you need to know. If we’re going to get into it then an insert is the main absorbent component of your nappy, so for something like an all-in-one this is the absorbent part attached to the PUL (waterproof outside layer). Or for a pocket nappy the insert is the main thing you are stuffing into that pocket. A booster is something separate that is used in addition to the insert to boost the absorbency. Some nappies come with boosters as well as the main insert part, some do not. Pretty much all nappies are designed to have a booster (of whatever brand etc.) added to them. A good booster can turn a nappy from a leaky nightmare to a reliable one.
This Lighthouse Kids Signature nappy is a great way to explain the difference. The insert is the absorbency which is stitched to the shell, this is irremovable. However it also comes with a small booster which can be added if and when desired, but is a separate item.
But the different words really aren’t anything to worry about. They just absorb wee.