Do Docker images save the memory state?

Very new to docker, apologies for the trivial question. I'm currently using a VM and creating live snapshots (which of course save the state of the memory, etc), such that when I revert its at that exact moment. Do Docker snapshots work in a similar way? If I snapshot it with a running application will it restore to that same state?

The CRIU project is working on technology which will make it easy to checkpoint and migrate containers, including RAM snapshots.

No. It saves "layers", which are essentially overlays on the file system, with some other magic for environment variables, ports, etc. No memory state is saved whatever.