A pdf article here, Medieval Arrowheads from Oxfordshire, by Richard Wadge has some relevant information for your query.
An image (plate 2) gives us a classification for one type of crescent broadhead, the Jessop H2:
The H2 type of crescent or 'forker' broadhead is discussed here (all emphasis mine):
Two examples of the H2 type have been found in Oxfordshire, and are
perhaps the oddest looking English hunting heads. One of them was
found at Woodstock (see Plate 2). Both heads could have been shot from
substantial bows as part of arrows made for repeated use, since they
are pierced for retaining pins. The purpose of these heads was almost
certainly for shooting birds, particularly large water birds, although
they could also have been used for small game like rabbits. A more
fanciful suggestion for the design of these heads is that they were
used at sea for cutting rigging. While it has proved possible to cut
ropes under tension with these heads, the practical likelihood of
doing so from a moving ship, given the tendency of these heads to spin
slowly, is extremely small. Rabbits, hares, and other animals were
also hunted with blunt-headed arrows. A major problem when hunting
birds, even large birds, and small game using arrows fitted with small
sharply pointed heads like those discussed below, is that the arrow
might pass partially through the game without knocking it down,
although the arrow shaft might deliver the fatal blow. Pictures have
appeared in the national and local press of large waterbirds, such as
swans and geese, with pointed crossbow shafts stuck in them, but they
were still able to feed, if not to fly. Secondly, arrows with sharply
pointed heads are much easier to lose, since they go deeply into brush
or can bury themselves in a grassy surface. These big crescent heads
would be less likely to do either, because the head would catch on the
brush or the ground, leaving the arrow lying on the surface. Since
these heads could be fitted with retaining pins, it was more likely
that the arrow would be recovered complete and ready for reuse.
So we have agreement by the author of Archery in Medieval England: Who Were the Bowmen of Crecy?, as well as an explanation as to the utility of this type of point for this application.