I understand that cottage cheese, cream cheese, and ricotta are all quite similar, and much of it has to do with how you handle removing the whey, or what you do with the curds afterwards.
But cream cheese is more like yogurt. You put the culture in the milk, add some sugar to feed it, heat it until barely warm and store until it thickens and can be separated from the whey by straining. The process is similar for both, just not sure if they use different cultures.