Key Points
On a Force Play the runner must reach the base before the fielder tags either the runner or the base the runner is forced to.
On a Tag Play the fielders need to tag the runner before that runner reaches and touches the base.
The Rule Book Says
A FORCE PLAY is a play in which a runner legally loses his right to occupy a base by reason of the batter becoming a runner.
A TAG is the action of a fielder in touching a base with his body while holding the ball securely and firmly in his hand or glove; or touching a runner with the ball, or with his hand or glove holding the ball (not including hanging laces alone), while holding the ball securely and firmly in his hand or glove.
Mechanics
On a Force Play, watch the fielder's foot on the base and the runner's foot (or hand) touching the base. Listen to hear the ball hit the glove.
On a tag play, watch the ball in the glove as the tag is applied. Know the position of the runner in relation to the base.