When ACPI S4 was first created, there were two versions: "S4OS", and "S4BIOS". In "S4BIOS", the dumping of RAM to disk is handled by the BIOS rather than the OS; this makes the implementation much easier since it means that the OS disk driver can be suspended rather than needing to figure out how to dump itself (and worse, restore itself) to/from disk.
Thanks for that, I had no idea! It sounds like I've been using S4OS with Linux. Do you know what the difference is between S4BIOS and Intel Rapid Start? They sound very similar to me. I'm wondering how the BIOS identifies, when it powers on, that it should resume and where it should read the contents of RAM from.
Yes, S4BIOS hasn't really been a thing for a long time -- once Windows supported S4OS (and didn't use S4BIOS even if it existed, since they quite reasonably didn't trust BIOS authors to get it right) all the BIOS authors said "this seems like a useless feature" and stopped providing it.
No idea about Intel Rapid Start. I don't really deal with that side of the system.