Two-dimensional chromatography is a common term, meant to denote two modes applied to one sample in series. That is, separate once, then separate each fraction another way.
On a TLC plate, that's easy to visualize, just rotate 90 degrees and do the same thing again with different eluents. But now, with advanced switching and automated peak selection, 2-D HPLC, for example, is becoming pretty hot.
Two-way is something I've never heard of, but it may be an older way of describing the new 2-D HPLC. What context can you give us about the terms?