Kortzfleisch uses the term "Jäger" for all the infantrymen of the corps, and "Scharfschütze" (sharpshooter) for the rlflemen, maybe based on Teichmann:

https://books.google.de/books?id=CDxYAAAAcAAJ&pg=PA34

Wachholtz, who in 1810 became commander of the riflemen company, uses "Jäger" only in connection with the rifle company.

On p. 141, writing that he quotes directly from Wachholtz, Kortzfleisch gives the etat of the corps as "1140 Jäger", whereas Wachholtz himself (link below), writes "1140 Gemeine" (privates, literally: commoners):

https://books.google.de/books?id=3CZhAAAAcAAJ&pg=PA419

I suspect that Teichmann's and Kortzfleisch's usage is an anachronism, but can't prove it