If you think that these two terms are almost the same, then you are right. Rogaine is known to be the brand name of this medication, while Minoxidil is known to be the generic form. If you would like to know more about the effects, most people say that they are exactly the same, so you do not have to worry about which one you need to get.
People who are on a budget may choose Minoxidil more because this is the more affordable option. The active ingredient for each drug is almost the same amount for every product that you will get. Make sure to ask your doctor for recommendations just to be sure.