Ear-enclosing headphones (over-ear) enclose the ear without touching it. They are the largest type of headphones and are particularly suitable for use at home.
Over-ear headphones (on-ear) rest on the ear with their usually slightly smaller ear cushions. This design is particularly suitable for mobile use.
On-ear headsets (single-ear) offer the advantage that the surroundings remain noticeable even during a telephone call, as one ear remains "free".