Merge Request and Pull request basically refers to same thing. Tools such as GitHub and Bitbucket choose the name pull request since the first manual action would be to pull the feature branch. Tools such as GitLab and Gitorious choose the name merge request since that is the final action that is requested of the assignee.
Pull/Merge requests are created if you are working in a feature branch and wants to merge your change in main branch(eg. Master branch). The merge requests serves as a code review tool and if your code reveals shortcomings/issues anyone(usually other developers) can commit and push a fix.
Life cycle : You create a branch, fix some issue or add a feature, create a pull/merge request, then you assign it to someone, he/she will review your fix and can accept/reject the pull/merge request.
Please note that a merge/pull request should not be confused with the “git merge” or “git pull” command.