Attachment is often described as the main obstacle to enlightenment, and as the cause of suffering and reincarnation. Religious philosophies such as Buddhism and Hinduism, among others, have many teachings on what are the main types of attachments, how to overcome them, etc. I will not repeat these here, it is easily available knowledge.
All attachments are psychical in nature. Even attachments to sensory sensations and physico-bodily needs are mainly psychical, for it is the psyche that clings in a desire-emotional manner. The body simply has needs and tendencies whether the psyche has an undue attachment to them or not. Attachment, therefore, really is of a psychical nature.
Now perhaps we can try to distinguish attachments according to the dual nature of the psyche: desire-emotional and mental. Usually, the psyche functions as a unit: We think of something that evokes a rise of desires/emotions. Or a desire (or an emotion) arises within consciousness, for whatever reason, and plunges the mind in a train of thoughts related to that emotion. Even though the psyche usually functions as a unit, some attachments are more astral (meaning the realm of desires/emotions, feelings, sentimentality, etc.) in nature. We get attached to what is pleasant. Or negatively attached to what is unpleasant. It is automatic, in the sense it doesn't really require thought. According to the astral response to anything, we seek to repeat or to avoid, hence the attachment.
Attachments that are more mental in nature are more linked to beliefs, opinions, to the way we view ourselves and the world. Religious beliefs, political, cultural, or group affiliations, create all kinds of mental attachments in people. If we change a mental attachment like a belief, it is usually replaced by another that might be more fitting to circumstances, more mature, less limiting.. but remains nevertheless a mental attachment. Eliminate all belief, and perhaps the mind can become a vehicle for the expression of truth only. But this is quite rare.
Of course, this is a very brief and archetypal view of the subject of attachment. It may seem like almost all psychical activity stems from, participates in, and furthers attachment, and therefore karma. This is essentially true. It will all gradually cease once we come to our spiritual senses, and fully realize the nature of consciousness, the soul, which is entirely devoid of psyche.