"What is the difference between southern and northern Shaolin styles?"
Well, to some degrees, not much, because, it's all basically Shaolin. Northern Shaolin, which is, the Shaolin. But there are some significant differences.
Shaolin gong fu tends to use a lot of legs; low stances, low kicks, mid-range kicks, and high kicks. They believe that the legs are more powerful than the arms (not to difficult to understand that logic), so they use more legs in the movements. The arms are primarily for blocking and feinting, though there are punches and strikes associated with the upper extremities. When the arms are used, they are used more for speed than they are for power, and they are used at almost complete extension; the elbow remains slightly bent at the end of most strikes. Some strikes have a completely straight arm as the end result, but they tend to be rare.
Southern Shaolin style tends to be more of the opposite. The legs are not used as much, and the stance is more upright. The leg movements are not as complicated as those in Shaolin (northern) style; the arms tend to be used more. And the use of the arms tends to be different also. When striking with the arms, the arms usually do not go to complete extension; they remain bent at the elbow even more so than in northern style.
So, southern style, more upper body, shorter strikes. Northern style, more lower body, longer upper body strikes. Wonder why?
Well, there are two versions of this story. Legend has it, that back in the seventh or eighth century, after the Japanese invaders were turned back (with the help of the Shaolin temple monks), some of the monks stayed behind in Fuzhou, Fukien province, where the battles were fought, to build a temple to commemorate the actions of their fallen comrades. Apparently, one of the monk leaders who stayed had been wounded in the leg, and was therefore unable to practice his gong fu as he had been taught. He, like most of us normally do, adapted to his situation, and converted his practice of gong fu to a more upper body style. Thus, more arms, less legs.
The other legend had it, that this monk just had bad feet, and therefore, upon being away from the Shaolin temple, refrained from practicing his gong fu in the manner in which he had been taught. Bad feet creates a style that is still practiced today. Not exactly a romantic notion, so, we'll try to stick to the other story.