Half Moon is a lunar phase coinciding with neap tides, which are often easier for seafarers than spring tides. This would apply to the first quarter and last quarter moon; in both cases, half of the moon's disk is lit. A crescent is a geometrical and symbolic moon shape.
Half Moon can also refer to:
Halve Maen or Half Moon – a Dutch East India Company ship with which Henry Hudson explored parts of North America
Half Moon – a German ship that sank off the coast of Florida in 1930
USS Half Moon, a United States Navy seaplane tender in commission from 1943 to 1946
USCGC Half Moon, later WHEC-378, a United States Coast Guard cutter in commission from 1948 to 1969