What JDiver mostly focused on was transportation providers.

But there are also credit card providers that have their own programs, and confusingly some of them call the units in their own programs points while a few call them miles. In the case of credit card providers' programs, there is no difference, it's just marketing language. So for example Capital One's "miles" and the "miles" on the new Discover Miles card are just points programs that choose to call their points "miles".

The origin of the term "miles" in airline programs is because you would earn one mile for each mile flown. That is still somewhat true at some airlines, but not that true any more at other airlines. So more and more the term is historical.

Thus the answer is very complex and difficult to give in general. It's much easier if you name the specific programs you're interested in.