Deadlifts are like Squats, except instead of the bar on your shoulders, it's on the floor in front of you, and you pick it up off the floor until your legs are straight (just like Squats), with your arms still straight. It's hanging down with your arms straight, which is why it's called a "Dead" lift.
Stiffleg Deadlifts are where you bend over, legs straight -- the exact way all jobs tell you NOT to pick things up off the floor. That's not to say you can't train your body that way; after all, the vast majority of people who work menial physical jobs, don't work out or lift weights on a regimen, so they usually screw their bodies up, so their backs, hamstrings, etc. get so out of shape that lumbar disks, etc. burst when they try to perform Stiffleg Deadlift-type activities.
Regular Deadlifts are, as said, just like Squats, except you use your arms & hands to pick the weight up -- just like in real life. How many times in real life do you pick something up like a Squat, with the object already on your back/shoulders? Only maybe in football or in a fight, where you bulldog into somebody. Otherwise, you usually pick stuff up off the ground with your hands. If you do this, then Regular Deadlifts will help you get stronger at it (& vice-versa).
Regular Deadlifts include Conventional and Sumo Deadlifts. Conventional Deadlifts are where your legs & feet are close, and your hands are wider than your feet. Sumo Deadlifts are where your legs & feet are wide apart, and your hands are closer, inside your feet. Sumo Deadlifts mean you don't physically lift the weight as far a distance, because the weight is closer to the ground at the top of your lift, than in Conventional Deadlift. Usually people lift more weight when doing Sumo, therefore, but some people are actually stronger at Conventional Deadlift, due to body leverages. You should probably train at both styles.