Actually a double move is a specific action. You can get up from prone and then move, but its just not a "double move". This would take up a move action and a standard action just like a double move does.
From PHB pg 284:
"Double Move
On your turn, you can move twice if you take a move
action instead of a standard action. If you take the
same move action twice in a row—two walks, two runs,
two shifts, two crawls—you’re taking a double move."
That "If" makes the double move type of action one of multiple legal possibilities. At least the way I'm interpreting it.
A double move has extra benefits, such as ending a move action in an allies space (because you aren't done moving that turn). Or getting circumstantially more movement in difficult terrain (due to rounding issues)
Following a move action with a different move action simply doesn't grant these benefits.