One of the characteristics of the English language is that for many words there are two alternatives - one coming from a Norse or Germanic root, the other coming from a Latin root.
So, the two English nouns for a place where a corpse is buried are 'grave' (German)and 'tomb' (Latin).
Sometimes a word coming from the German root is spelled exactly the same as a word with a totally different meaning coming from the Latin root - 'grave' being a case in point.
The English adjective 'grave' meaning solemn or serious comes from the Latin gravis.
The fact that grave (= solemn or serious) music is played at funerals has nothing to do with the fact that the corpse will be laid to rest in a grave (= tomb).
As for the modern "pop" usages that you mention - I prefer not to go there!
Graham