Pairs of paths with the same source and target but with no other nodes in common are called parallel paths, at least on the computer science side of things in graph theory -- you can google the term to get some relevant CS papers, but I couldn't find a wikipedia article on parallel paths.
If your paths are allowed to share nodes other than the source and target, I would suggest something like "piecewise parallel paths". With this terminology you can simultaneously get the idea across and score cheap points for alliteration.
As requested in the comments, here is a reference
Jwo et. al., Characterization of node disjoint (parallel) path in star graphs (1991) see here.