Here's some very basic basics:
"Real" road pedals have a much larger cleat than the type of pedals and cleats that can be used with mountain bike shoes. People who know more and ride more than I do say this larger cleat/platform combined with good road shoes provides better support and more solid connection.
There are several types of cleats in this category, I know nothing about the + and - of any, except my WAG is that it's mostly a matter of personal preference and that any will work really well. One down side is that these kind of shoes/cleats are kind of difficult to walk in because you have no heel on the shoe and a large cleat under the ball of your foot - not really designed for walking. If you wear your shoes only for biking, it is not a problem. Guys I ride with who wear this sort of shoe/cleat change into the shoes right before they ride and change out of them as soon as they're done.
If you fit this profile, you might try this type of shoe/cleat/pedal.
There are also various types of pedals that use cleats that can be used with mountain bike type shoes - shoes that have a treaded bottom and can be more easily be walked in. The generic term is "SPD type", but actual SPD-compatable pedals aren't the only type. The major difference with "real" road cleats is the size. The mountain cleat could roughly be covered by a US Half Dollar coin, so it is small enough to fit within the tread pattern of mountain biking shoes. That's why you can walk more easily, the cleat doesn't affect the contact betwen your shoe and the ground when you're walking. Road cleats are much larger and totally exposed.
I've only ever used the SPD-type cleat and mountain shoes. I have fairly stiff soled shoes, and have never noticed any problem with lack of stiffness or "hot spots" under foot which might indicate lack of a large enough platform. When I bought them, I more or less tried to find the mountain shoe that looked pretty much like an equivalent road shoe, exept with the treaded sole. (they are Specialized Comp - which comes in a road and mountain version, very similar, moderately priced) I have also never inadvertantly popped out of the pedal - another possible deficiency of this type of cleat. I am not a huge, powerful rider and don't race or sprint. I do stand on the pedals as hard as I can to start up at intersections and get through traffic though. I guess you could call that sprinting.
I have two sets of pedals for these cleats - "road" version which look like road pedals and clip in only on one side and "mountain" pedals which clip in on both sides. I do not think the performance or weight is different in any meaningful way. The mountain pedals are said to be easier because you don't have to flip them up to clip in. However, with about 3 times practice, the road pedals are easy enough to use (similar in difficulty to the old clip/strap pedals - flip them over and get your foot in). I just like the way the road-version looks on a road bike, but like the two sided attachment for mountain biking.
If you want a single pair of shoes for both road and mountain biking, and want the option of reasonably walking in the shoes, this is a good option.