Usually when you MAKE contact with someone it is for the FIRST time. Just contacting someone is to get in touch with them. You could also use making contact with someone if you are reuniting with a long lost friend after several years. Hope that helps :)

If you contact somebody this means that you are going to contact them implying that you haven’t before or haven’t for a while. To be in contact with means that you regularly speak with the person - quite difficult to explain but hopefully this makes sense!