Modern digital consoles have totally changed the workflow of live sound, and have given engineers tons of tools to help them have a great show. At the same time, high end analog consoles have a sound that can't be replicated by digital consoles - yet.
There are, of course, many differences between them, but here's an overview:
This is just one section of our How to Use a Mixer course. The rest of it is available for free on this site - just click here to see it all.
I do encourage looking for offline editors to get a sense of how different digital consoles work. Of course, the only real way to get to know a console is practice, so take the opportunity to get some hands on time when you can.