Troddel, Faustriemen confussion?

[panzeriv]

According to Brian Davis' "German Uniforms and Insignia 33-45" page 70
The Troddel was worn my Infanterie, etc. while the Faustriemen were worn by Kavallerie and SCHUTZENREGIEMNTER.

Does this mean that the Schutzen Regiments of the early war (39-40)
Panzer Divisions would have worn the Faustriemen and not the Troddel?

Thanks
Scott