I hope you don't mind me answering. With the caveat that different people have different ideas and opinions about what AD's are and different types, so the answer i give might be different than the answer someone else would give. Even experts don't agree on it! This is my understanding of it, based on what I've been told when my children have had therapy and been dx'ed with attachment issues (not disorders though)
Attachment disorder is having enormous difficulty or the inability to form relationships, especially the one with your primary carer/s. AD is the blanket term. Anything more descriptive, I would say is a type of attachment disorder. I have seen and heard of children being diagnosed with 5 different types - RAD (inhibited), RAD (disinhibited), Avoidant AD, Ambivalent AD and Disorganised AD. Or just RAD or AD without any qualifier.
The way I see it, is the different types are like different types of any medical or mental condition. In AD it's about the childs patterns of behaviour and way of relating to people. Taking RAD as an example, if there are two children and one is dx'ed with disinhibited RAD and the other with inhibited RAD, they both can't form attachments, but they behave differently - the first child might be extremely friendly to strangers and try to cuddle them for instance, whilst the second would not want to cuddle or initiate things like that with anybody, stranger or parent. The three other types of AD are related to the three insecure types of attachment (disorganised, avoidant and anxious/ambivalent).
I think if you live in the US, you are probably more likely to get a RAD dx but in the UK you are probably more likely to get an AD diagnosis, with a qualifier like avoidant. My DD2 was identified as having an (insecure) ambivalent attachment style, and if she had been disordered, she would have got a dx of ambivalent attachment disorder, not RAD. There is some overlap as well, especially between the 3 AD labels and the two RAD labels, I've seen children dx'ed with disorganised attachment disorder who would probably have been dx'ed with RAD (disinhibited) if they'd been seen by different people. But a child with avoidant AD will have different behaviour patterns than a child with ambivalent AD, and a child with one subtype of RAD different behaviour patterns than a child with the other. Same basic condition though
Hope that makes even a bit of sense, that's how it was explained to me