The differences are many. In FUE we harvest the grafts one by one. The scarring is minimal, and is hard to notice because the area is hair bearing. And it allows for the patients to wear their hair short post-surgery. It allows for having many grafts, and is a comfortable surgery.
FUT is the abbreviation for follicular unit transplant. In FUT, we do not harvest the grafts one by one, rather we extract a big donor area. The cut in the donor area is covered with sutures, and you may not want to have short hair afterwards because the scar is noticeable. It is also hard to harvest many grafts.
Follicular unit extraction is widely preferred nowadays.