Having a good friend who is a life coach, let me explain it like this.
First, calling yourself a "psychologist" requires a university degree in psychology, at least in the US. Most people who sell their services as psychologists have an advanced degree in psychology, in addition to their first degree. A psychologist often helps people with what might be called "problems". They help the client solve the problem and thus improve their life.
A "life coach" has no educational requirements, but they may be psychologists as well. Most life coaches are older people with a lot of life or business experience. Rather than focusing on solving explicit problems, they focus more on helping people reach their potential. So you could say they focus on "opportunities" rather than "problems."
The line between them is not a clear division. There is a lot of overlap in the people they help and the situations the people are in.
Both can use the same evaluation methods and problem solving techniques, many of which are taken from research in psychology.
This is only a rough explanation, but I hope it is somewhat helpful.