There is a big difference there, not only semantics.
If I have my private bank account, I can draw as much from it as I like and spend it on whatever I want. I can buy materials and make them into something new, but the whole thing is mine from start to finish, there is nobody else involved. Of course, I can only use as much money as I have.
On the other hand, if I am on a business account, it is not my money I am dealing with, it is my employers money. To a degree, I might be free on how I spend it, but there are plenty of restrictions on when and how I can use it. If I want to use some of the money on myself, I will have to pay it back, or in the worst case, I will get fired. If my employer doesn't like what I am doing, he'll just close the account, and I'm left with no money to spend whatsoever.
And the DV magic works pretty much exactly like this. Evocation and a lot of other powers are a private account, sponsored magic and any other form of sponsored powers are business accounts.
Both kinds can use magic as you described, moving energy from one place to another, but that doesn't make all magic external. Hell, most of the time, the wizards we see are throwing around magic powered by their own will, not their surroundings. Harry does it a few times in order to either accomplish a secondary effect (freezing a lake by pouring the heat energy into a ball of fire) or to use it to power a spell beyond what he could do with his will alone.
The original Star Wars force is private, I think, because it doesn't just go away if the force wants to. You need to be able to use the force, but that just means you need those microsomethings in your body that allow you to manipulate an otherwise natural phenomenon.
The force I want for the true believer jedi knights in my game is supposed to be an external power, bestowed on individuals by the powers that be good (sometimes known as the white god). Of course there could be a young kinetomancer out there, thinking he is using the force, and in effect, he kind of is. But that's another kind of magic, not the one I am planning in this thread.