The difference between a tendon and a ligament is that a tendon connects muscle to bone, while a ligament connects two bones. Tendons let your muscles move bones, whereas ligaments stabilize joints.
Both tendons and ligaments are fibrous tissues designed to connect parts of your body. This tissue is tougher and less flexible for tendons and stringier and more elastic for ligaments. However, both tendons and ligaments require some degree of flexibility to accommodate movement; rigid tendons and ligaments would prevent basic body movements.
When tendons and ligaments are stretched beyond their basic capacity, they become damaged. For tendons, this can result in tendonitis, which occurs when the tendon becomes torn. This damage causes the tissue of the tendon to inflame while it heals; as a result, tendonitis causes swelling and soreness, as well as temporary loss of muscle function.
Ligaments also suffer damage when stretched beyond their limits. As with tendons, this can result in tears of the tissue. Ligament tears weaken the joint and threaten its integrity. For example, tears of the anterior cruciate ligament, or ACL, in a person's knee are fairly common among athletes. This tear destabilizes the knee, and requires many months, and sometimes surgery, to heal.