When a runner does not tag up on a caught batted ball, it is neither a force play nor a time play. It is an appeal play. The appeal is made by touching the runner or base with the ball. Contrary to many other appeals (e.g. a missed base) no announcement of the appeal is necessary, because the appeal is obvious.
If the appeal is the third out and a preceeding runner was trying to score, there may also be an associated time play: the run scores if the third out occurs after the runner touched home. Contrast that to a force situation-- if the third out is made by a forced runner before he reaches his advance base, no run can score.
A force play can only occur when first, first and second, or all three bases are occupied at the time of the pitch. A forced runner can be put out by tagging him or his advance base, but that is not the definition of a force play.