Simple answer.

Non-profit doesn't aim to make any money, they usually are started for a cause and live on donations. Because of that, they may be regulated under charity and have different requirements in some countries. Think NGOs and some charities in your area.

Social enterprise on the other hand, can also be started for a cause, run like a "normal" business, using business models and strategies to get to financial or operational sustainability. Typically, their primary goal is to make a difference in their cause, thus creating a positive impact to the society. They aim to make profit so as to achieve sustainability, but the goal of social impact is higher ranked than profit.

In my humble opinion, all enterprises should be social because all of us should aim to create positive impact to the society.