Target archery- The most mainstream type, used for formal competitions and the Olympic Games. Archers shoot at familiar colour zoned targets from a shooting line on an open range. Target sizes and distances are dictated by choosing particular archery rounds suited to a competitor’s age and ability.
Field archery- This is shot following a course set over various terrain. Targets are placed up and down slopes, in woodlands, across water, and the like, set at random distances which may or may not be marked at the shooting point. This is the nearest we come to the bow hunting experience in this country, which is illegal. Scoring zone target faces are used, however, a form called “3-D” archery uses life sized polystyrene models of game animals with kill zones marked on them.
Clout shooting- Archers shoot from a set distance, at a zoned scoring area marked on the ground. In days gone by this would have been a large cloth or “clout”, in old English, laid on the ground. A lot of clubs use this as a break from target shooting and is a popular form of competition. Clout Archery Distances Shot
Flight shooting- This is a specialised form of the sport where the archer uses knowledge of the physics of the bow and arrow in order to shoot the arrow as far as possible. more
As archery is such an old discipline, you will find many and varied ways to challenge the archers ability have been devised, mainly as an exercise to develop combat skills in times gone by. A lot of books on archery describe these in greater detail.