Is this algorithm actually a graph-traversal algorithm?
There seems to be a bug in the first algorithm which is fixed in the second algorithm, namely the first EXPLORE explores only the starting vertex and its neighbors, but nothing beyond that. However, the first algorithm at least explores the entire graph; the second one only explores the connected component of $s$. The second one also doesn't bother to initialize the array visited.

I strongly suggest that you try and understand what these algorithms are doing. It could help running them manually on a few examples. You could also program them and have the programs print out the actions performed by the algorithms.