I agree with BALIX. Pretty much the same thing.
I would use "Route Direct AAA" if you were flying on your own navagation (not on a heading assigned by ATC)
I would use "resume your own navigation to AAA" if you had previously been on a heading assigned by us.
Either way i want you to head towards AAA now.
You are correct in saying that if you were given route direct to AAA, BBB, CCC, then we expect you to go now to AAA then BBB then CCC
Hope that helps to clear it up a bit.