Do different web sites use different size avatars to maintain user avater image in several sizes?

I will give two examples what I mean:

1. At Fluther I have my avatar image in small size like you see here near my question and answers, but in my profile page I can see my image in another big size, where I can upload a new image if I want to.

2. At Facebook when I write status I have my image at one size, but If I add a comment my image size is smaller and not at the same size at all.

My question is how web sites in the real world are saving my user picture. Are they saving my picture in all the sizes needed to be display, or there is only on size picture is saved in DB and in every page the picture is being calculated to the size needed.

It looks to me a lot of work to caculate the pictures of all the users needed to be display in one page. I just want to know what is the solution to that problem and what web sites really do with my only one picture I use.