(1) Filesystem backup. Sometimes people will use this generically for any kind of backup, but "dump" is a very specific tool. Dump is ancient stuff - it goes way back to the very beginnings of Unix. You would almost always find older systems using dump for backups.
A good sign that you've found dump is tapes labeled "/dev/root" etc. If that's followed by a number from 0 to 9 (an indication of the "dump level"), then it's a pretty sure bet.
Restoring from dump tapes is done with "restore", and that's one of the least user-friendly programs ever written, especially if you just need certain specific files. All the power you need should be there (though I think I recall very early versions where you had to figure out the inode number you wanted before you could get it back!). Contrast this early restore man page with a more modern Linux version.
But don't use this stuff. As Linus Torvalds says, "Dump was a stupid program in the first place. Leave it behind." (see Opinions on Dump)
(2) A memory dump. A program "dumps core", which means it creates a file suitable for a debugger that has its state information: what its memory looked like, register settings etc.
(3) Examine an object file. See dump(CP)
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