No, not at all. Thanks for explaining your context, as without that, I would have been wondering what you meant, as both those words have quite a few different meanings. Promote doesn't 'cause' anything. You are trying to persuade somebody that something is good. It only works in that context. It's similar to 'advertising'. You can promote something, but the person then decides what they want to do. Prompt is just for a reminder. You are just helping someone remember that something needs to be done. They have already decided that that is what they will do.

They have similar meanings but are used in different contexts

To promote something is to make it be known like to advertise it or as an increase in ranking "I promoted my youtube channel to get more viewers." Or "My boss promoted me to assistant manager." To prompt something is to bring it up in conversation or to cause something to be known. "The death of the politican prompted a thorough investigation by the FBI."