pail (n.) Look up pail at
mid-14c., of uncertain origin, 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, stewpan" (see pan (n.)).

Old English had pægel "wine vessel," but etymology does not support a connection. This Old English word possibly is from Medieval Latin pagella "a measure," from Latin pagella "column," diminutive of pagina (see page (n.1)).