[capableweb]

Other answers are already good, just offering yet another difference.

Parameters is something that gets set indirectly via training, it's kept within the weights of the model itself.

Context is what you as a user passes to the model when you're using it, it decides how much text you can actually pass it.

Being able to pass more context means you can (hopefully) make it understand more things that wasn't part of the initial training.