It is a long debate. Both fish were initially lumped into the 'Cichlasoma' catch-all group but they have since been given their own genus -- Mesoheros.
Mesoheros gephyrus and Mesoheros ornatus are both currently considered valid species, but it is thought that all fish listed as M. ornatus are actually M. gephyrus and that M. ornatus is not currently in the hobby. M. ornatus come from a remote area that is dangerous to collect in, so they have not been introduced to the aquarium trade.
There have been tireless threads with lots of arguments, pointing out that some fish in captivity are more yellow with black markings, while others are more red and have less markings, looking something like a cross between M. gephyrum and M. festae. But that could be down to collection locale differences, as cichlids of the same species can vary in color and appearance depending on where they're collected in their range. There are also a couple of photos of fish that are fresh out of the river, and there is still debate over what fish is shown in the photos. Are they festae? Are they true ornatus? Who knows. It's impossible to say for sure with just the photos.
So no, based on current taxonomy, they are not the same fish, but all of the ones you're seeing online are likely to be the same species: Mesoheros gephyrus. A lot of exporters and sellers are still mislabeling the fish as M. ornatus even though they almost certainly aren't.