Once upon a time, you put simple /dev/sdX names in your /etc/fstab. These days that's boring and deprecated, and so there are a large number of different identifiers that you can use here. Since I just confused myself on this today, I want to write down what I know and looked up about the various levels and sorts of identifiers, and where they come from. What I care about here are identifiers that are tied to a specific piece of hardware or data, instead of where that hardware is plugged into the system (or the order in which it's recognized during boot, which can totally jump around even when no hardware changes).

Some filesystems have labels, or at least can have labels, and years ago it was common for Linux installs to set labels on your filesystems and use them in /etc/fstab via LABEL=.... This has fallen out of favour since then, for reasons I can only theorize about. ExtN is one such filesystem, and labels can be inspected (and perhaps set) with e2label. Modern Linux distributions seem to no longer set a label on the extN filesystems that they create during installation. Just to confuse you, extN filesystems also keep track of where they were last mounted (or are mounted), which is different from the extN label, and some tools will present this as the 'name' of the filesystem.

(e2label is effectively obsolete today; you should use blkid.)

Many filesystems have UUIDs, as do swap areas, software RAID arrays, LVM objects, and a number of other things. UUIDs are what is commonly used in /etc/fstab these days, and can be displayed with eg 'lsblk -fs'. The blkid command is generally the master source of information about any particular thing. Like labels, UUIDs are embedded in the on-disk metadata of various things; for extN filesystems the filesystem UUID is in the superblock, for example. Where software RAID stores its metadata varies and can matter for some things. Note that software RAID has both a UUID for the overall array and a device UUID for each physical device in the array.

(As blkid will report, GPT partitions themselves have a partition label and a theoretically unique partition UUID. These can also be used in /etc/fstab, per the fstab manpage, but you probably don't want to. The GPT UUID is stored as part of the GPT partition table, not embedded in the partition itself.)

Physical disks have serial numbers (and World Wide Names) that theoretically uniquely identify them. Where they're accessible, Linux reads these via SCSI, SAS, iSCSI, SATA, and so on inquiry commands, and uses this information to populate /dev/disk/by-id. In addition to actual disks, generally anything that appears as a disk-like device with a UUID (or a name) will also show up in /dev/disk/by-id. Thus you can find things like software RAID arrays (by name and UUID), LVM physical volumes, and LVM logical volumes (by name and ID).

(I believe that some USB disk enclosures don't pass through the necessary stuff for Linux to get the disk's serial number.)

Sometimes this can get confusing because the same object winds up with multiple IDs at different levels. A software RAID array or a LVM logical volume that contains an extN filesystem has both a UUID for the filesystem and a UUID for the array or volume, and it may not be clear which UUID you're actually using unless you look in detail. Using blkid is generally fairly clear, fortunately; lsblk's default output is not so much from what I've seen.

(If you're looking at an /etc/fstab generated by an installer or the like, they generally use the filesystem UUID.)