Ligaments are collagen structures that connect bones-to-bones and provide joint stability. Knee ligament injuries, or "sprains," can vary in severity and location. Some may require surgery depending on the goals of the specific patient. Often times bracing and a period of rest are adequate.
The meniscus is the "gasket" between the thigh and and shin bone, one on the inside and outside of the knee. Meniscus injuries are often from twisting, however with age, degenerative tears may develop. Just like ligament injury, there are a variety of different tears and not all meniscus tears require surgery. If they do, sometimes the meniscus is repaired and sometimes it simply requires removal of the diseased portion, allowing you to get back to activity quickly.