The International Weightlifting Federation (IWF) sets the 20kg men’s and 15kg women’s bar, along with the technique bars used to teach the lifts. The International Powerlifting Federation sets the competition bar at 20kg, with a shaft between 28mm and 29mm, a maximum overall length of 2.2m and grip markings 81cm apart.
Those figures have become the default across UK commercial gyms, which is why the standard rack is almost always 20kg. The men’s and women’s distinction exists for competition categories rather than as a rule about who should lift what.
Everything else on the list is down to the manufacturer.