'Grenadier' is a honorific starting from (sometime in 1942) I believe.
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German motorized infantry troops were renamed 'Panzergrenadiers'. Mot. Infantry divisions were also renamed: "Panzergrenadier divisions"
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Yes, thanks. And the term Volksgrenadier was coined later to inspire the soldiers even more (Volk = people).
edit: Not to be confused with Volkssturm, that is sth. completely different and atrocious.