T. barbieri is surely the most common aquarium Taxiphyllum - and aquarium moss at all, so it's quite likely that the 1st moss is T. barbieri indeed. But I'm afraid only bryologists could verify it. E.g. I know a Taxiphyllum from Thailand with the information that it was IDed by Prof. Tan as T. taxirameum - I can't tell it apart from T. barbieri superficially.
It seems that also regularly branched species others than Vesicularia montagnei are sold as Xmas Moss, but I don't know what species they are.
The pics 3 and 4 here: http://www.flowgrow.de/pflanzen/Vesi...-Moss-218.html
show an emersed moss that should be V. montagnei, I've obtained it as "Java moss" and checked it with a microscope, the leaves match the pics and description of V. montagnei here: http://www.aquamoss.net/Christmas-Mo...stmas-Moss.htm http://sea.nus.edu.sg/aquatic-mosses.pdf
=> roundish leaves with rather short, sharp tip and broad thin-walled cells. But submerged, the features are rather like in V. dubyana...