Pail

wiktionary

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From Middle English payle(“wooden container”), of uncertain origin.

Possibly from Old English pæġel(“wine vessel, container for liquids, pail; liquid measure”), from Proto-Germanic *pagilaz, equivalent to peg +‎ -le. Compare Middle Dutch pegel(“half-pint”), Danish pægl(“half-pint”).

Alternatively from Old French paielle(“pan, cooking vessel, liquid measure”), from Latin patella(“shallow dish”).

etymonline

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pail (n.)

"cylindrical bucket," mid-14c., paile, probably from Old French paele, paelle "cooking or frying pan, warming pan;" also a liquid measure, from Latin patella "small pan, little dish, platter," diminutive of patina "broad shallow pan, stew-pan" (see pan (n.)).

The sense evolution might have been affected by Old English pægel "wine vessel," but etymology does not support a direct connection. This Old English word possibly is from Medieval Latin pagella "a measure," from Latin pagella "column," diminutive of pagina "page, leaf of paper, strip of papyrus fastened to others" (see page (n.1)).