At the risk of setting off massive disagreement, I will offer my own understanding of native plants, as a non botanist. A native plant is a natural, indigenous inhabitant of a particular area. It is native to a specific geographical zone (like an area colored in on a map) or a particular point within that zone. The geography is an essential component of the core meaning. It is where the word "native" can be applied to a given plant. It is also subject to debate and modification and revision pending the introduction of new facts.
A plant is not native to a given place if humans took it from somewhere else (where it grows naturally, or grew naturally earlier in human history) and introduced it there. It is not really helpful to overthink this, beyond the limits of curiosity anyway. The natural range of a given species will tend to change gradually over time, especially as human activity limits its potential (eg. by grazing or clearing for agriculture/development), generally resulting in reduction. This is particularly evident in our ecosystem (California coastal chaparral) which has been widely disrupted and fragmented and paved over, but much more so north of the border and much less so here in Mexico, so those differences are evident by comparing the two places, just an hour or two apart.
A plant is endemic to a given place if it occurs naturally in that place only. The key factor implied by the use of that word is restriction, meaning that species does not naturally occur elsewhere. It is a way of implying exclusivity, which of course is dependent on our basic knowledge of natural populations, and where they do not occur (or did not occur in the recent past, relative to human history anyway). "Endemic" is not a synonym for "native", it is a clarification of native that only has meaning when applied to a specific restricted area. An entire area colored in on the aforementioned map, or a political region encompassing that area, but not any given point within that range. A given cactus may be native to northwestern Baja California (right here, where it grows just up the hill from our house) but endemic to the Californias, for example.
I hope this clarifies any misunderstanding. I can't tell you how many times people have shown up on this site asking "Is this a weed or a plant?" (spoiler: it could very well be both). So not everyone starts with the same understanding. Other people have wanted to add mushrooms to the plant database (spoiler: different kingdom). The more we explicitly lay out what these words mean (native, endemic, invasive) and explicitly lay out the geography associated with them, the less misunderstandings there will be.
