The complexity class PPAD is usually defined by stating that End-Of-The-Line is PPAD-complete.
End-Of-The-Line is a search problem. The input consists of a directed graph in which each node has in-degree and out-degree at most 1. The graph is given by a polynomial-time computable function $f(x)$ that returns the predecessor and successor of $x$. In addition, one is given a node $v$ with a successor but no predecessor. Find a node $t\ne v$ that has no successor or no predecessor.
Recently, I heard a different definition of PPAD. As far as I recall, it was based on the following problem.
A directed graph (again specified by a polynomial-time computable function) and a node whose in-degree is not equal its out-degree is given. Find another node with this property.
Clearly, End-Of-The-Line is a special case of the latter problem but is the latter problem really more difficult to solve? My question is this:
Are both problems complete for the same complexity class PPAD? If yes, why? If not, what is the complexity class resulting from the second problem?