Yes, they are one and the same work. "The Manifesto of the Communist Party" is the same work as "The Communist Manifesto." It simply is the full title of the work translated from the original German...
The major elements of The Communist Manifesto are: That society consists of the struggle between different social classes. In the industrial at present the classes are the bourgeoisie (the owners and...
Karl Marx had an International Communist Party and he wanted to make a, as we would call it today, a party constitution. He also wanted to define communism in "The Manifesto of the Communist Party".