A fall is technically defined as an unplanned move from one level to another. So a person could fall to the floor, fall into a chair, etc.
What you always want to determine are the causes of the fall and the effects of the fall. If someone says they tripped over the cat, that's one thing. If they say they got very dizzy and woke up on the floor, that's a cause for concern. In terms of the effects, people over age 65 are at higher risk for problems such as fractures and brain bleeds.
In people over 65, falling is something their health care provider should be assessing regularly. The #1 risk factor for falling is having had a previous fall, and falls can be a major cause of health issues and even death. A number of different things can cause falls, including factors such as health status, vision issues, layout of the home (for example, throw rugs are very dangerous for causing falls), and even medications - the effects of medications are increased in people over 65 as the brain is more vulnerable and the liver and kidneys are less efficient at breaking down and getting rid of medications. Falls in people over 65 are considered a "geriatric syndrome", meaning they're a problem that's not uncommon in people in this age group. Of course, people can fall at any age, but as I've indicated, falls tend to cause more problems in people over 65.
lemongrove - I have also seen a fall referred to as an FDGB, namely "fall down go boom".