I actually did a thesis on this type of material, so you came to the right person! Gothic Rock is a style of post punk. Much like the animal categorizations of family > genus > species, music can be categorized into genre > subgenre > style. Genre is basic structure of the sound (things like bar progression, pacing, etc), subgenre is a more specific sound structure (things like key, scale), and style is (as the name implies), how the music is stylized (distortions, instrumental modifications, and so on). Although gothic rock is post punk, not all post punk is gothic rock. Post punk is a larger umbrella than just goth music. Gothic rock is the particular stylizing of post punk.