Yes, adults have attachment styles, too, and they can have problems with attachment. A child with an insecure attachment style is not considered to have a disorder unless the problem is very severe in which case they can be diagnosed with Reactive Attachment Disorder. An adult with very severe attachment problems, on the other hand, might be diagnosed with a personality disorder but not RAD. Personally I'm not a big fan of how the DSM breaks things down, but I figure it's helpful for people to know in understanding how they might have gotten or not gotten a particular diagnosis.