The API example[1] gives several sources: USDA.gov, CATMINAT, PlantNet, GBIF, RBG Kew.
There might be other sources, but I don't know about all of these in detail, so I'm not sure. Several of those sources have their own APIs, I think this service's offering is joining everything together.
There are around a million names for plants, but due to changing scientific hypotheses, limitations of science and communication centuries ago, new technologies (DNA sequencing etc) and so on, over 600,000 of those names are synonyms for other plants.
I was going to give the synonyms for Solanum tuberosum L., the potato, but it has tens (maybe hundreds) of them. Look at the bottom of the infobox: https://en.wikipedia.org/wiki/Potato