Skeleton: Function is to support the body, create an anchor for muscles and act as a shield for vital organs. You have 206 bones in your body, which contain osteoblasts (making new bone) and osteoclasts (breaking up old bone.) Your skeleton has the capacity to change over time, which is why we can improve bone density with exercise and nutrition.
Muscles: Their function is to move bones, put simply, and are arranged in pairs which contract-extend to create movement. There are involuntary and voluntary muscles, and your largest muscle is...your gluteus maximus (which in conjunction with your gluteus medius can affect your hips, low back, and general life comfort if too weak or too tight).
Tendons: Primarily attach muscle to bone, and sometimes attach muscle to muscle. They are composed of collagen, and an injury to a tendon would be called a strain (although there are plenty of other ways to injure a tendon). Most of the movement in the hand is executed by muscles that originate in the forearm, connected to the hand through tendons.
Ligaments: These attach bone to bone, acting like the duct tape keeping your bones together underneath all of your other tissues and organs. If you think of a model skeleton with metal rods keeping it standing up, your ligaments provide a similar support. If you injure a ligament, it is a sprain (as opposed to a strain). Some of the most known ligaments are those of the knee-the ACL, or anterior cruciate ligament, for example.
Therefore, tendonitis, is an inflammation of a tendon, which connects muscle to bone. One of my teachers describes the pattern as, "Overuse in one direction will lead to weakness and stiffness in other areas." Treatment can be complicated, depending on the area afflicted, the movement pattern that caused the tendonitis, and the overall state of the tissues surrounding the injury. I personally have found bodywork, acupuncture, and rest to be the most helpful in my recovery process, but seeking a medical opinion, especially in nerve entrapment situations, is important.