come with me= accompany me Examples: Come with me to the football game. Come with me to the police station. Follow me= walk/ drive behind me or obey me [ if used in a military sense] Examples: Follow me in your car so you don't get lost. "Follow me! Attack!" yelled the general to his troops.

Come with me is a request whereas follow me is kind of a command.

They are the same.

They could mean the same. 'follow me' implies that you are going to lead them somewhere. 'come with me' doesn't necessarily mean you are the one showing them the way,it just means a request to accompany them. However you could ask them to 'come with you' and they would be 'following you' at the same time.

both mean the same thing