Are protozoa, protists, protoctista different classes of organisms or simply different names for the same?
These terms are all somewhat obsolete as taxonomic terms, but they may still be used to describe certain groups of organisms.
The term "protist" is used informally in two different ways. One usage refers to the paraphyletic group consisting of all eukaryotes other than the animals, plants, and fungi. The other usage is to refer to those eukaryotes that exist as independent cells or, if colonial, do not form colonies with differentiated tissues.
The term "protozoa" is used informally to refer to the "animal-like" protists, i.e. those that are non-photosynthetic and motile.
Wikipedia gives a good summary of how these terms were used historically.
Protozoa as of 2017 is how Microbiologists define one of the six categories of microorganisms. Microbiologists classify microorganisms into: Bacteria, archaea, fungi, PROTOZOA, algae, and small muticellular animals
Then you have how Biologists categorize things, and they classify not into 6 groups but into three groups --> Bacteria, Archaea, and Eukaryote
Then you have the further refining that Biologists use which is Kingdom- which is Bacteria, Archaea, Fungi, Protista (old name for this kindom USED TO BE protozoa), Plantae and Animalia
SO in 2017 , if someone says protozoa, they are no longer talking a kingdom they are talking about a microbiological category for a microbe. If they do say protista, this is the correct kingdom terminology for the protists... which make up the category !
According to Wikipedia Protist and Protoctista are equivalent. "The term protozoa is used to refer to heterotrophic species of protists that do not form filaments." - from the same wiki.