Common words have special meanings in the social sciences. Not in this class. Get used to it because things work better with the social science meanings. Influence is our umbrella term. Any time a source deliberately attempts to change a receiver's thoughts, feelings, or behaviors, influence has occurred.
Persuasion is under the umbrella as a special case of influence.
When a source deliberately uses communication to try and change a receiver's attitude, then persuasion has occurred. Attitude is a person's evaluation of an object of thought. Persuasion, not influence, seeks to change attitudes because . . . Wait a minute, this is HiTech, baby. You're living fifteen minutes into the future.