Depending on the git management application you use, one of these terms is very familiar to you.
In fact, they both refer to the exact same thing. Think of them as synonyms.
When you are used to work with a certain git management application like Github or Bitbucket where the term pull request is used. Changing to a git management application like gitlab is confusing because of the term merge request that is suddenly used.
Because the first action involved when applying your changes on another branch is a pull command. Some git management applications choose for Pull request. Others will refer to the last action in the process, hence the name Merge request.
A better name for me would be Change request.
Because that’s what it is. A request for a change to a certain branch. Notice the importance of good naming to avoid confusion… just like in code.