That is simple. Goshawks are types of hawks. The set of things that are goshawks are a subset of the set of things that are hawks. The set of things that are hawks (family Accipitridae) also includes eagles, harriers, kites, buzzards, sea-eagles, old world vultures, etc. A subset of family Accipitridae is the genus Accipiter that includes the goshawks and sparrowhawks and a few others that are given their own name. So yes all birds that are in Accipiter are essentially Hawks even though it may be called a Goshawk, or Sparrowhawk etc.
The set of things that are hawks (family Accipitridae) does not include the falcons & new world vultures, etc.
Philip
