At the beginning of the Kree-Skrull War, millions of years ago in Earth time, the alien Kree established a station on the planet Uranus, a strategic position between the Kree and Skrull empires. Through their work at this station, they discovered that sentient life on nearby Earth had genetic potential invested in it by the alien Celestials. Intrigued, the Kree began to experiment on Earth's then-primitive homo sapiens by splicing Eternals DNA into Cro-Magnons.
So, Inhuman DNA is originally a cross breed of Eternals and Cro-Magnons.
Marvel Universe goes on to explain that the Inhumans historically selectively bred to strengthen their genetic pool and avoid unwanted mutations.
However, The Inhumanity storyline has shown us that there were people with Inhuman genes living on Earth without ever knowing their true nature.
Similarly, in the MCU, Skye only recently learned of her nature.
If Inhumans have different DNA than normal humans, why can they not be identified until after exposure to the Terrigen Mists?