A Bates number is a page-level label, applied in order, that never repeats within a matter. One page equals one number. The label usually combines a prefix identifying the producing party with a zero-padded counter, for example SMITH-000123.
The three names describe one practice. Bates numbering emphasizes the sequence, Bates stamping emphasizes marking the page, and Bates labeling is the phrasing used in e-discovery load files. A page that is bates stamped, bates labeled, or bate stamped is the same page with the same mark.
Because the numbers run in an unbroken sequence, opposing counsel, the court, and your own team can point to a single page out of hundreds of thousands and everyone finds the same document.