Tab
late Middle English: perhaps related to tag1.
wiktionary
First attested 1607, of uncertain origin.
Apocopation (shortening) of (variously) tabulate, tabulator, or tabulation.
Likely to have been formed by clipping the Geordie pronunciation of the word tobacco or alternatively from the brand name Ogden's Tabs.
Clipping of tablature
Clipping of Cantab, from Cantabrigian, from Latin Cantabrigia(“Cambridge”).
Clipping of tabloid.
Clipping of tablet.
tab (plural tabs)
etymonline
tab (n.1)
"small flap or strip of material," c. 1600, possibly from a dialectal word, of uncertain origin. Often interchangeable with tag (n.1). Compare also Middle English tab "strap or string" (mid-15c.), Norwegian dialectal tave "piece of cloth, rag."
tab (n.2)
"account, bill, check," 1888, American English colloquial, probably a shortened form of tabulation or of tablet in the sense "a sheet for writing on." Figurative phrase keep a tab on is recorded from 1890.
tab (n.3)
1961, shortened form of tablet (especially one of sugar containing LSD). As an abbreviation of tabloid (newspaper) it is 1990s slang. As a short form of tabulatorkey of a typewriter (later computer) it is recorded from 1916.
tab (v.)
"designate, label, name," 1924, earlier "affix a tab to" 1872 (implied in tabbed), perhaps an alteration of tag (v.2). Related: Tabbing. Also see tab (n.1).