Is a clinch takedown the same as a throw?

No. A throw is a trip or toss from the lock. A clinch takedown is the shot or drive from the same phase.

When should I shoot from the clinch instead of from range?

When they stuff the open-space shot or they are high-blocking in the pocket. Close first, then wrestle.

No Grapple Advantage, no stamina, or they denied on time. Build the meter, then go.

A shot from the lock is harder to read than a shot from the center. That is why wrestlers close the distance first.

How to takedown from the UFC 6 clinch when a shot from open space keeps getting stuffed.