I don’t expect to get one definite answer here, but Google can’t give me one either. Some websites say they’re your second cousin, and others say they’re your first cousin once removed. I’m trying to figure out some family tree stuff so I need to know the difference between the (groups of) terms.
Your first cousin’s child is your first cousin once removed. The only reason anyone calls it anything else is because the terminology is confusing and they misunderstand it. Your child and your first cousin’s child will be second cousins.