There's no discernable difference between YouTube.com and Youtu. Be, and the videos displayed on each one is all the same. Youtu.be is just a shortened web address, which is also owned by Youtu.be main page. Shortened web addresses are a good way of making it easier for people to recall it immediately.
This situation occurred at a time when web addresses were starting to grow longer, and the possible combinations were all being used up by a plethora of different people. This problem is insignificant to such a popular medium as YouTube.com.
This shortening just accomplished a reduction of three letters. YouTube was able to secure certain things. Namely, an address that is yours and only yours, and it cannot be procured by anyone else. Its other ambition is to follow the trend of using unusual domain hacks or names.