There are two basic types of tendons, flexors and extensors. Flexors allow a joint to bend and tend to be on the front of the horse's limbs while extensor tendons extend a joint and tend to be on the back of the horse's leg. Major extensors are the main extensor tendons (or common digital extensor tendon) and the lateral extensor tendons. Major flexor tendons include the superficial flexor tendons (closer to the skin) and the deep flexor tendons (closer to the bone). There is something called a bursa which is related to tendons and ligaments but is neither. A bursa is a sac filled with synovial fluid. They are found near bony projections such as the point of the elbow and point of the hock. It helps protect areas of bone where there is little more than skin to provide protection.
There are several types of ligaments. Collateral ligaments are on the sides of a joint, they are short spans of ligament to connect short bones. They can be thought of as band-aids that help hold the bones together against moving in a way they weren't meant to move (think of how you can flex and extend your elbow but you can't really move your elbow from side to side). Another type is the check ligaments. They prevent a joint from overflexing. Annular ligaments surround a bone for support. Capsular ligaments surround joint capsules.
One very important ligament is the suspensory ligament. It begins beneath the knee and splits near the sesamoid bones to wrap around the pastern joint and helps support the fetlock much like a sling. This is an important bone to condition because it can tear under stress if the horses is overworked before it can handle it.
The hind legs are attached to the body by the pelvis (made up of the ilium, ishium, and the pubis which is near the femur socket). Next comes the femur and the tibia and fibula which are fused together. The femur, tibia, and fibular, together with the patella make up the stifle joint. Horses can lock this joint which is how they manage to sleep standing up (called the stay apparatus). Next come the 6 hock bones, the most important of which are the calcanius and the talus. Theses two bones are what allows this joint to move. After the hock the leg is made up of the same structures as the foreleg after the knee. The hind cannon tends to be longer and the splint bones may take longer to fuse.