Can you educate me on high profile v low profile tires?

I’ve tried to read up on the internet, but I find conflicting information. I now know what it means, but I have several questions:

We just bought an Escalade. I love the rims, but Rick says they have low profile tires on them. He said it makes for a rougher ride than high profile. However, on the internet I read that low profile tires make for a smoother ride. Seems to me like the high profile tires would make for a smoother ride. So which is it?

Also, can we put high profile, 20” tires on the existing rims, or do we have to buy all new rims? We have 17” tires now.

Anything else you want to share with me about tires would be great.

Thanks.