In the Buddhist tradition, the word "attachment" and "detachment" are frequently used. People can get very confused about what that means because we can sometimes think, "Aren't you talking about something that the Buddhists say we shouldn't do? We shouldn't attach to things, right?"
Attachment theory is something quite different, but there's also an interesting alignment with it. It's like the difference between connection and grasping. Attachment theory describes the bond between one human being and another, our biological drive for safety and how we are hard-wired for connection.
The Buddhist concept of suffering comes from grasping after things in life and feeling like we can't continue without obtaining something, and how that leads to suffering.
Interestingly, I think that kind of grasping comes from a lack of early bonding also. One of the consequences of insecure attachment is an attempt to over-grab, to grasp too much, to hold on tightly, to fear that something won't be present.
Attachment has to do with safety, an internal sense of safety and the ability to move out into the world and explore it with curiosity and aliveness. The Buddhist sense of attachment is that when we do have that sense of safety, we can move out into the world and it isn't based on fear. It's based on security and then there's less of that kind of grasping.