Joining two different tile
Extruded tile edging is typically installed underneath the tile before it's laid. If your existing tile is at a higher level, this probably won't work as you'll want the outer face of the edging oriented toward the lower tile. It is possible that the hem on the inner face will be tall enough to do the job, however. 



Another option would be a beveled marble transition strip (threshold). By placing the bevel toward the lower tile, you'd have a nice finished elevation change.