Sure! Every goth is different, everyone identifies with a different thing in the subculture. XD
Besides, not all of that is correctly associated with "goth." Death metal isn't the least bit gothic, death metal is just death metal. Marilyn Manson isn't necessarily even gothic, either, at least not according to many people who like traditional gothic music. Rather, what it is is that a lot of goths like his music. Heh.
Enjoyment of inflicting pain is sadism, which is sort of more associated with fetish culture, Sadism & Masochism (S&M) and what not. That said, a lot of goths get into fetish culture, so whatever. Hahah. So there are a lot of contradictions and things that overlap and are convoluted, but regardless: I advise you to never go to VampireFreaks. They would call you a poser and rip you to pieces there. Seriously. Some goths are SO uptight about what's gothic and what's not it's not even funny.
I consider myself gothic, even though I wear no make up, I have yet to dye my hair black, and most of my favorite bands have a heavier emphesis on metal than traditional "goth." I identify with the subculture because most of the things I like ARE gothic in some way, because my writing is gothic (I write about vampires, succubi, etc.), because I adore the macabre, because I'm usually pretty depressed, because I love gothic movies and artwork, and because I frankly think goth girls are really hot. Hah.
As for Goth vs. Emo, the differences are primarily in the music and in the clothing. In fashion, Emo boys almost always comb their hair over their eyes and wear super tight girl jeans (and maybe complain about their dicks hurting later). Goths, however, have much more variaty, ranging from the "industrial"-associated PVC and fishnet and latex and plastic hair extensions, to the romantic, vampiric, elegant Victorian wear. Emo music sounds nothing like any music that is the least bit gothic--compare My Chemical Romance or Hawthorne Heights, both blatantly emo bands, to any band that's considered gothic. This includes 80's traditional goth bands like Bauhaus or the Cure, gothic metal like Moonspell or Theatre of Tragedy or even Nightwish, industrial-gothic bands like Collide or Skinny Puppy, and even industrial rock like Marilyn Manson or KFMDM or Orgy (none of which are exactly gothic but are enjoyed by many goths nonetheless). No music that's associated with emos sounds at all like the music that's associated with goths.