My hypothesis: Getting out of the pool let’s the surface tension of the water pull most of it off of you as you exit the pool, while a shower coats you evenly in thousands of individual droplets that cannot connect with each other to become heavier
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.
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