S0ix is the new standard for W10 and beyond, in which the operating system attempts to itself shut down as many peripherals as possible, downclock the CPU, shut off unnecessary cores - but stay in ACPI S0. Basically just run normally, but try to be as power efficient as possible, following how mobile phones do things. Its big advantage is that it allows for varying levels of background processing (and eg. network connectivity) that just aren't possible with traditional S3. The downside is that it needs great hardware support within the OS and that it's a complex, system-wide effort to implement (like, needs application cooperation). Linux's S0ix support (via s2idle) is quite mediocre right now.
S3 sleep is the same ACPI-driven suspend-to-RAM mode that PCs have been shipping with for decades, in which a complex rube goldberg of DSDT and platform controller pokes ends up making a CPU stop running, having saved its entire state into RAM. The upside of S3 sleep is that it generally works, unless a machine's ACPI DSDT is terribly broken (which still unfortunately happens). The downside is that it's pretty much binary (either you sleep or you don't) and that you can't control what wakes you up. I mean, there's some ACPI mechanisms for it, but they're limited and janky.
New Thinkpad BIOSes can let you choose between either exposing old-school S3 via ACPI for non-W10 systems, or enabling S0ix functionality for W10. The default is generally S0ix/s2idle.
See: https://www.kernel.org/doc/Documentation/power/states.txt
That being said I have not owned a laptop in the past decade that I trusted to sleep when running Linux. I've had nothing but problems with things like WiFi not coming back up or the machine randomly waking up in the middle of the night.
Those machines running Windows are much better. But really the only machines I trust to wake and sleep reliably are Macs. I haven't run into major sleep/wake issues on Mac laptops in twenty years of owning them.
https://brauner.github.io/2018/09/08/thinkpad-6en-s3.html
I recently bought a T14, which also has this option.
(It enables S3 sleep.)