Why does the water in the pool look a different color than in the glass?

Basically what's happening is that you need a lot of water for the effect to be noticeable. Water absorbs light, but only when there's enough depth. In a small glass, light passes through just fine because the distance is really short. In a swimming pool, when you look down, the light has to travel meters of water before bouncing off the bottom and coming back up, and it loses a lot of energy along the way.

What some people say about red light being absorbed is technically correct, but I'll put it in a way that makes more sense: water absorbs red and orange colors especially first, so after passing through several meters, those colors just disappear and what you see is what's left, which is basically blue and green. That's why when you put your hand in the pool you see it a different color than when you look at it from above, because you're seeing the light bouncing off your hand from different angles.

If you filled a bathtub pretty deep or a large container, you'd start to notice a slight bluish tint too. The effect gets more pronounced the more water there is in the path of the light. It's not magic, it's just physics: lots of depth kills the warm colors and leaves you with the cool ones.

The amount of water is what matters here. When you look at a glass, light passes through just a few centimeters of water without any problem and you see it as completely transparent. But in a pool with several meters of depth, that same water absorbs the red light and lets more blue light through, so what you see is that bluish color. It's the same effect you see in the ocean, just amplified.