It has a single origin. Sayayin culture. Remember Vegeta was a sayayin, and he and his friends introduced that type of armor when they landed on earth for the first time.
But Frieza's troops also wear them, and so does Frieza himself (in his weakest form, before he breaks it) despite looking down on the Saiyajin. So are you sure it was the Saiyajin who introduced it to Frieza's empire, and not the other way around?