Do the terms mycophyta and fungi represent the same thing?

Yes.

Mycophyta and fungi refer to the same group of organisms.  These include mushrooms, yeasts, moulds, rusts and the alike. Mycophyta or fungi are a division of simple eukaryotic organisms which lack chlorophyll. They hence have to rely on other organisms for their nutrition. They are unicellular and usually have tubular filaments or hyphae. They can reproduce both sexually as well as asexually. The result of sexual reproduction is a large number of spores which help in the propagation of the species.