Parsnip is a surprisingly interesting word for its humble meaning. It comes to English from the Old French pasnaie, which is from the Latin pastinare, meaning ‘to dig up the ground’. The verb pastinare is derived from the Latin pastinum meaning a hoed field, or the action of hoeing, or a two pronged dibble tool.
The end of parsnip is different from pasnaie because it was merged with the older English neep, which was used for turnips, and is derived from another Latin word, napus, meaning turnip or rapeseed. The Latin napus itself comes from the Ancient Greek νᾶπυ (nâpu), which meant mustard, and probably came from Ancient Egyptian.
By comparison a turnip gets its turn- from the shape, as though it had been turned on a lathe.