[ncallaway]

Mentour Pilot (as others have mentioned in various other comments) does a great job explaining this.

On the 737 the trim adjusts the entire rear stabilizer (the entire horizontal structure of the tail), while the elevator is a sub-component of that stabilizer.

So, when you adjust the trim, it's a much larger surface area that is moving. Ultimately, the stabilizer just has more aerodynamic control that the elevator, due to the larger surface area.

I have no idea why the design is that way, though.

[inferiorhuman]

I have no idea why the design is that way, though.

Cost, maintenance, weight, etc., probably. The only jet airliner I can think of that uses an "all-flying tail" is the Lockheed L-1011. Nearly every other plane you'd be riding on will have a big stabilizer and a smaller elevator.

[phire]

Redundancy too.

If both redundant hydraulic systems to the elevator fail, or the elevator gets stuck for other reasons, the emergency procedure is to control pitch with just the stablizer trim alone.

[inferiorhuman]

Presumably you could have a redundant drive system for the combined stabilizer/elevator. The L-1011, for instance, had a safety record Boeing should be envious of.