What is a difference between a migrant and a refugee?

Migrant - a person who moves from one place to another in order to find work or better living conditions.

Refugee - a person who has been forced to leave their country in order to escape war, violence, persecution or natural disaster. A refugee has a well-founded fear of persecution because of race, religion, nationality or political opinion. In many cases, they can't return home or are afraid to do so.

Source: https://www.unrefugees.org/refugee-facts/what-is-a-refugee/

So, difference is that migrant isn't forced to move, it is his/her free will to do it, and refugee is forced for the sake of saving life by horrific event that is happening in their country.