It's essentially just to different ways to add to a users reputation count.
By pressing the plus rep (Or minus rep) button, (The little star in the left corner of all posts) you can add to or extract from the poster's reputation count, and the amount of points given/taken depends on your reputation power. However, in the cases of neg reps, it will only be half your rep power. Example, if I give someone rep, they'll be granted eight points, but if I neg rep someone, his rep count will decrease by four points.
The Thanks button is essentially just a way to give rep without using the actual button. It can never decrease reputation points and can only be used on threads, and when used, it will raise the receiver's rep points by five, regardless of the giver's rep points.
If you have any more questions, just say so.