A bill is a class of agricultural implement used for trimming tree limbs, which was often repurposed for use as an infantry polearm.
In English, the term 'Italian bill' is applied to the similar roncone or roncola, but the Italian version tended to have a long thrusting spike in addition to the cutting blade.
The bill is similar in size, function and appearance to the halberd, and might be said to represent convergent evolution to fill a common niche: a pole-arm with a point to thrust with, a hook to drag with, and a spike/axe to cut with.
The English increasingly transitioned to pike and shot formations from the mid 16th century, but kept the billhook in use in the same capacity as other armies used greatswords and halberds.
Lansdowne MS 56, attributed to Lord Burghley, states that ideally infantry formations should consist of 50% shot, 30% pikes, and 20% bills.