Neither Boeing nor Airbus make their own engines. They get them from CFM, GE, Rolls-Royce. Like everyone else. That's not the differentiator.
But it just costs insanely much to get an airliner certified. Even Boeing has been held back by its clients demanding a shared type certificate for the 737max which caused all those deaths due to mcas.
There were of course more players but they've been bought up. And some emerging brands that are excluded from our markets due to sanctions like the Chinese Comac and the Sukhoi Superjet. The superjet is particularly affected because some of its systems were designed by western companies like Honeywell and they've had to make last-minute replacements after the Ukraine war that didn't exactly work out well.
And there's some other players. Embraer is creeping closer to the 737/A320 market.
But anyway so it isn't just Airbus and Boeing really.