Frogs were made with and without the retaining straps. Personally I have never understood the need for them, the Sg84/98 as used during the Nazi era was well secured in it's scabbard so it isn't required to keep the bayonet from falling out of the scabbard but it does keep the bayonet and scabbard from moving around some. You will see some of the retaining straps removed by cutting on original frogs.
The Variants with the buttoned grip strap. Are know generaly, as cavalry pattern. The strap prevented the sidearm from swinging about on the wearer. Due to extra jolting & movement when mounted on a Horse. (Well, that was the theory,reason for the strap!.....)