MTB pedals are mainly SPD (though there are some other makers about). The cleat is small, triangular and fastened to the shoe with 2 bolts (thats the important difference). The cleat is designed to be recessed into the sole of the shoe, making it easier to walk.
Road pedals are SPD-SL (or Look/Time/others). The cleat is much bigger, usually plastic and stands proud of the sole. It's fastened with 3 bolts in a wide triangle arrangement. The cleats can be difficult to walk in, and wear much faster the MTB cleats.
Most shoes will only take one or the other cleat type, although there are a few that will do both. Road shoes tend to be narrow, have incredibly stiff soles and are a swine to walk in.
MTB shoes have more tread (usually) and often a more normal appearance - many would pass for trainers/hiking shoes. The soles tend to be slightly more flexible (but still stiff) and much easier to walk in. They're almost always a lot heavier though.
Theres also a small number of "touring" shoes. These often use a SPD MTB cleat which is only slightly recessed into a stiff sole. You can walk short distances OK, but the on-bike side is more pronounced.
Road pedals themselves are larger platforms, usually single sided (so you have to flip them into place before clicking in). Spd Pedals are smaller, can be single or double sided, and can be set up with a flat platform on one side to allow you to wear normal shoes.
Each system has it's advantages. The SPD is better if you need to walk anywhere, and arguably for stop/start riding such as a commute.
The SPD-SL is better for longer rides, as the larger area of the cleat and stiffer sole can prevent "hot spots". SPD-SL are also perhaps slightly more efficient at transmitting power.
Personally I use SPD "touring" shoes on the commute, and SPD winter boots when needed. They offer the best balance of stiffness, and I can walk across the office car park without looking like Bambi on ice.
For longer summer rides, SPD-SL shoes come out - more comfortable and a bit cooler.