The short and simple answer: "save" is a verb meaning "to protect from danger", "safe" is an adjective meaning "not in danger".
The policeman saved the old lady from the criminal. The old lady is safe.
There are a few meanings where the words are quite different, for example:
It's important to save money (NOT: "I have safe money in the bank", "save" can only be a verb when it means "keep money")
However the simple rule "save = verb, safe = adj" should work most of the time.