Yes modern karate is only roughly 100yrs old.
TKD has roots older than karate, but I believe most of the way it’s been trained the last…30-40 years makes basically shotokan with fewer punches.
The founders of the original kwans all trained karate or kung fu and nothing else. any other "roots" claimed are basically invented out of thin air. its "taught to them in secret by mystic monks on mountaintop temples" credibility level stuff. pure nationalistic "we cannot admit we learned it from the hated chinese and japanese" BS. there may have been native unarmed fighting systems in korea, but they did not survive to be anything but mere inspiration to TKD
As for karate, as we know it today it is about a hundred year old, but it grew out of older systems from okinawa with very strong influences from china.
Karate wasbutchered by american servicemen in Japan. anyone REALLY think a okinawan master was going to teach an american the deep secrets of his beloved art a mere few years after the battle of okinawa in 1945? really? in the servicemans spare time during a year or so?
civilian casualties after the battle and bombing might have been as high as 150K out of a pre war population of 300K (killing almost every skilled karateka still on the island, I might add). Rape was rampant during the occupation (not to mention the horror stories from the battle) and seldom punished by the army (and therefore not by anyone). american soldiers was NOT highly regarded.
A karate teacher might take the occupiers money to survive, but he was not going to seriously teach him anything advanced.
And then those americans goes back to the us, founds schools and organizations and claims to be masters themselves.