There is a big overlap between tanks and SP Guns and the roles of tank/ armoured corps, anti tank and close support / assault artillery.
Indeed. Zaloga is technically correct as far as his statement concerns tanks (in the narrow sense of the word, i.e. turreted). Taken in a more general sense, his statement is however misleading, as it implies the absence of any armored, direct fire close support for German infantry.
This, as has been pointed out, was a role assigned to the assault guns.
In addition, it should be mentioned, that tanks often were (ab)used, normally by temporarily subordinating a company or battalion sized tank battle group to an infantry division or corps. Something the tankers hated and repeatedly pointed out resulted in little success and high losses. The infantry was not trained in cooperation with tanks, and vice versa, the tanks were not trained in close cooperation with infantry.
There was more to the unit than the equipment. The procedures and training played a part. Artillerymen and tank corps thought differently.
Good point. For the Germans, it seems that assault guns and tanks used different fire or ranging procedure.
To find the correct range and get their fire on target, assault guns used the bracketing procedure originating from their mother branch, the artillery (direct fire not withstanding).
Tanks, it seems, used a more direct procedure, based on the individual correction of each shot (miss).
In autumn 1943, some experts suggested that the assault gun ranging procesure was quicker or otherwise superior and that the tanks should adopt it.
That caused some "paper war" that can be traced from the records of
Generalinspekteur der Panzertruppen, but it seems the tank branch ultimately rejected the suggestion.
In addition, it seems assault guns had by default superior optics.