Differences in Short.
Basically, wine is a linux program that creates the proper environment for the .exe file you are trying to run. While it has helped many people run executables, it is not perfect. Some files will not work with wine. Although it is a linux program, you can use
Macports to use it on a mac, or get the winebottler/wine for mac
here.
Winebottler and Wineskin are both versions of wine, but made by different people. They both create bundle/native versions of the program, and are still not perfect. Wineskin is typically used for gaming, but will work with day-to-day windows programs. Winebottler is another version of wine, but does have some problems porting over complex executables.
All of these programs will run in Lion, as they are currently projects being worked on. Keep in mind that these applications are not the only options in developed to run windows files on mac. Some other common ones are:
Crossover
Cadega
Cider
Mono
*I have only used cider, a professional cross-platform gaming package. As I am not familiar with the other applications, I could be wrong as to what they do. You'll have to read the instructions to figure out how they work.
Hope this clears some things up,
mourginakis