They have similar meanings. 'Keep in mind' is more like a reminder, it's a more gentle way of telling someone to remember something. Or, it can mean to be more generally aware/cognizant of something.
'Remember' is a very standard, basic instruction. Sometimes, it can be annoying to be told 'remember' as it sounds more authoritative, i.e. like something that your mom or dad might tell you, maybe in a reprimanding sort of way.