Soft corals are the mushrooms, zooanthid polyps, Xenia, leathers, toadstools, and the like. These are soft in that they dont have distinct calcerous skeletons.
LPS stands for large polyp scleractinian(or stony corals. These have definate calcerous skeletons that the polyps are supported by. Examples of these are the hammer, anchor, torch, bubble, elegance, and most of the brain coral types.
SPS are small
polyped stony corals that are primarily skeleton with a thin layer of tissue and little polyps. These are the branching corals that you see in underwater scenes. These are represented by the acropora, millipora, montipora, seriotapora, hydnaphora. Sometimes refered to as "sticks" these are the high light loving calcium consuming corals from the reef crests.
BTW the terms SPS and LPS are mainly hobby distinction and not a valid scientific reference. A really good and inexpensive starter book that covers basics on corals is
"A Practical Guide to Corals for the Reef Aquarium" by Borneman and Puterbaugh. Usually less than $25 its cheaper than most corals and can save you from buying something you aren't prepared to keep. The new coral book by
Julian Sprung is a great companion to it.
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I dont advocate holding marine creatures for ransom but......since you asked
Doug, plank owner
http://hellreef.homestead.com/index.html
www.thereeftank.com/ubb/Forum2/HTML/000001.html 
