West as a adjective we can use before a noun (for example west London), as a adverb we use to ot towards the west ( for example to travel west, we live west of the city), as we use as a noun it is a direction you look towards in order to see the sun of down, one of the four pionts of the compass (There's a road to the west of here), the part of aby country, city etc. I I live in the west of Germany)
Westerly is a adjective and we use only before a noun; to, towards or in the west (in a westerly direction. We can also use it about winds which comes from the west.