Q:

What is the difference between off vs. from?

What is the difference between off vs. from? For example, I fall from the car or I fall off the car?

A:

"I fall from the car" means there was no specific relation between you and the car before you fell. 
In this usage it is more likely to refer to you being in the car. You could equally have been on top of it, or hanging from it.
"I fall off the car" means you were on the car before you fell. It is more specific in its usage as it indicates your relation to the car before falling.

