Conviction means to believe strongly in something, enough so to convince or persuade others. Commit means to entrust, put in a place for safekeeping or carry into action by choice. Consider the following examples.
Setting Expectations: I have committed and will attend the meeting.
Finishing a Task: I am committed to completing this project.
Determined: I am a committed to winning the game.
Devoted: I am committed to my spouse.
Simply stated, are you committed to your convictions?