Attachment seems to have more to do with emotion and feeling within/about a relationship. Dependency seems to be more a behavioral term.

Both can be healthy or unhealthy.

I can have a healthy attachment to my therapist: we get along, I appreciate his role as my therapist, I don't expect it to be more than what it is designed for. I can have a healthy dependence on my therapist: an ability to ask for help when I require help.

I can have unhealthy attachment: feelings/hopes/desires about wanting therapist relationship to be something other/more than it is designed for. I can have unhealthy dependency behaviors concerning my therapist: not using my own skills when I can; expecting T to "fix" me/save me or being completely unable to ask for help when really needed.