Asexual - someone who does not feel sexual attraction
Aromantic - someone who does not feel romantic attraction
Asocial - someone who doesn't feel platonic attraction
So, an asexual/romantic/social person wants to have friends and partner(s) but not sex. A sexual/aromantic/social person wants friends and friends with benefits (or casual sex) but no romantic partners. A sexual/romantic/asocial person isn't really into friends but very into having romantic partners who they have sex with. And then there are combinations like asexual/aromantic/social who don't want anything beyond friendship, asexual/romantic/asocial who have romantic relationships but very few friends, and sexual/aromantic/asocial who isn't really into people in general unless there's genitalia involved.
The reason I think there's a whole missing layer to the typology is that I've now encountered two different people who strike me as asocial. The first is definitely sexual and romantic but seems to have no need to go find friends to share feelings or knowledge or experiences with, and the other who is definitely sexual but not only seems to not understand the difference between romance and friendship (and of course, I was very little use explaining since I don't entirely get the difference either), but also seems to only value friends as activity partners with specific activities/interests in common. And it seems to fit in rather nicely in terms of scales of intimacy, both physical and non.
I'm pretty clearly asexual/aromantic/social. I'm not interested in sex or romance but I have a strong need to connect with people on a platonic level. I hope to someday find my very own queerplatonic partner who I can live with without all that messy relationship stuff.
Also: bonus comic about what being aromantic is like for at least some people