I'm assuming (that horrible, horrible word) that they are similar to 'block level' snapshots, similar to what other virtualization, backup, and storage vendors use. (VMware uses change block tracking and delta disks, Nimble and (IIRC) Veeam use change block tracking as well. If I recall how SQL server snapshots work correctly , it writes the old data that got changed to a seperate database file when a row is updated or added to a table.
I've not actually looked at AWS for anything, it's something of an anathema here at [RedactedCo]. Azure, if anything would probably leverage whatever methodology Hyper-V uses for snapshotting it's VMs, although I could be waaaaay off.
I find it ironic that they are charging for restores.