There are a lot of different terms that researchers in the field use: psychedelic (mind manifesting), hallucinogen, psychotomimetic (psychosis mimicking), and entheogen (god manifesting) are the main ones. Normally which one you use depends on:

- who you're writing for - what aspect of the drug experience you're trying to emphasize

In Griffith's study he uses the term hallucinogen, most likely just to expedite IRB/FDA/DEA approval. In general though the preferred term seems to be entheogen now at least for conversational purposes, because people find it less objectionable than hallucinogen or psychedelic for obvious reasons, and it also tends to be a good conversation starter for people who haven't heard the term before. The downside is that while most atheists seem not to be bothered by the term, a few are. And it's not always appropriate, e.g. it wouldn't make sense when dosing rats with LSD or whatever.