2 main factors here.

Time between getting out and wrapping yourself in a towel.

How much of your body is actually wetted.

The first means you have time to drop dry, before you grab your towel. It's only 10s or so, but you can shed a lot of water in that time.

The second matters, since you tend to keep your head out of the water in the pool, but soak it in the shower. Wet hair can hold a lot of water. Even if you don't dry your hair, the water will run down of the rest of you, as you dry yourself off.

Finally a proper shower thought in this community haha.

Soap.

Soap breaks the surface tension of water (allowing it to break up whatever is on you). Shower/bath water will spread more evenly across your skin than chlorinated pool water.

Post this on an ask science community, see what smart people have to say, and then get back to me, because I never really thought about it, but you're right

Personally, I don't notice this. It takes just as long to dry off from a shower as it does a dip in a pool.

I'd imagine your standard for "fully dry" is just different for each of these.

Maybe pool water is heavier? Shower water is aerated and is more sticky?