Perfect matching in a graph and complete matching in bipartite graph
These are two different concepts. A perfect matching is a matching involving all the vertices. A bipartite perfect matching (especially in the context of Hall's theorem) is a matching in a bipartite graph which involves completely one of the bipartitions. If the bipartite graph is balanced – both bipartitions have the same number of vertices – then the concepts coincide.

The term bipartite perfect matching is not standard – in fact I just made it up. Usually perfect matching just means a matching involving all the vertices.