Well the difference is simple; a social entrepreneur is one who sets up a venture to achieve some greater good aside from just the product and making profit. The drives I suspect are identical as for most entrepreneurs the money isn't the primary driver.
One of the aims is to solve some social problem, be that actual projects in the community or simply funding them.
It's a new name for something that has gone on for many years. see for example, Joseph Rowntree .. https://secure.wikimedia.org/wikipedia/en/wiki/Joseph_Rowntree_%28philanthropist%29
In one sense social entrepreneurship can be an attempt to lessen the imbalance created by legislation on both sides of the Atlantic that a company exists to maximise returns for shareholders. If you're required to maximise profits above all else then you're lessening your opportunity to do good, or may look favourably on cutting corners on, for example, environmental responsibility. (If it's legal, it's good enough). If the articles of the company and the mission build this in from the start, then more can be done.
I don't think it can be said social entrepreneurs aren't real entrepreneurs - the requirements are the same. The business has to succeed on the level of profit and customers or it cannot be self sustaining and achieve the social aims it also has. There's many cases of entrepreneurs trying to achieve something worthy with the money they've made, but I doubt the majority would see themselves as social entrepreneurs.
As to where you draw the line, I have no idea. There's a lot of shades of grey in between the extremes of profit at all costs, and all profits to social good.