Well, this should be an easy question bordering on stupid, but the thing is, looking around on the web, I'm finding conflicting information regarding what a "squat" is and what a "deadlift" is. One website's defiition of a squat seems to be the same as another website's definition of a deadlift. One website will basically say the difference is that a squat puts the weight up by the shoulders and a deadlift puts the weight by the knees. But another website will say one can put the weight with a squat either low or high and that the difference is how one has their legs.

So, could someone give some authoritative guide to each, how they are different, and the advantages of each?

I myself am interested because I want to increase my jumping and sprinting capability. My goal is not to be able to squat or deadlight my car but is ultimately to have powerful, explosive power useful in playing sports. Also, I just have dumbbells and don't plan to get a barbell unless there's an absolute need for one.

Squats and deadlifts are performed differently, but the weights distribution can be varied. For example, you can squat by holding a barbell frontward, over the back, or you can hold dumbbells to the side. Deadlifts can be performed in various ways too.

The main different is the following:

Squats: Bending the legs at the knee and hip level while keeping your torso straight.

Deadlifts: Lifting an object off the ground from a stabilized position.

Squat
Barbell Squat

Deadlift
Barbell Deadlift

For jumping power you could try a Good Morning with a jump at the end to improve explosive power
Barbell Good-morning

this can also apply to the deadlift check out CCRs link.

the squat and deadlift are two exercises that are great supplements in progressing to the snatch and clean/jerk. These last two exercises are fundamental in a speed and power program. Also, be sure to add in some hamstring exercises as they also contribute greatly to speed and power, especially sprinting. A great exercise that translates well to speed is the Romanian Deadlift. These exercises can be found in the links provided by CCR.
Most sprinters I know follow this routine:

Power Movement (snatch or clean and jerk)
Back Squat
Romanian Deadlifts