|endemic means occurring nowhere else, restricted or peculiar to a locality or region:
The Komodo dragon is endemic to an island in Indonesia.
(This example addresses the natural condition and rightly ignores the fact that
Komodo dragons exist elsewhere in captivity.)
indigenous specifies being native, not brought in from elsewhere, though the object or being may also occur somewhere else:
Tobacco is indigenous to the New World.
native implies birth or origin in a particular place:
The native Coloradan still marveled each fall at the native aspens.