Well, I tend to differentiate between types of music on a much coarser level then most. So at a root level, I would split my own musical preferences into something like:
1) Art music
e.g. baroque, classical, romantic, impressionist, serialist, post-serialist etc.
2) Folk/traditional music
i.e. regional or culturally based traditions of music
3) Popular Music
e.g. Rock, Chart, Metal, Rap, Hip-Hop
4) Jazz
e.g. Big Band, Bebop, Modal, Latin Jazz, Jazz Fusion etc.
I realise there is a lot of interplay and relationship between the categories but this is just the way I generally think about, understand and enjoy various forms of music.
In particular, I closely associate the various forms of music I am calling pop because they share many formal attributes and methods of production and dissemination. To name a couple:
i) mostly one vocal part and three to four instrumental parts.
ii) mostly song based forms e.g. intro/verse/chorus/verse/middle eight/chorus/outro etc.
iii) similar commercial models.
iv) lyrics are generally more important than in other musical forms.
v) mostly released in the album format with 8 to 12 or so 3-6 minute songs.
Of course these characteristics aren't totally unique but you have to organise things in your own mind somehow. I do see the difference between say a Death Metal band and Lady gaga - I just see the difference as being less profound then the difference between either and, say, Mahler.
Edit: Also, it is because I don't resent the majority of people calling things as diverse as gregorian chanting and post-serialist music all 'classical' because I understand what they mean when they lump the forms together in that way, even if I think they are more disparate than some of the items I consider to be 'pop' music
.