That's the basic gist of it. The effect isn't so pronounced after WW2 and the huge-upscaling in defense contracting, but prior to WW2 it was the norm. The USMC were equipped only after the US Army had been fully equipped etc. For example, the large majority of marines in the 1st division landing at Guadalcanal in August of 1942 were equipped with the bolt action '03 Springfield while virtually all of the Army units at that time, with the exception NG units stateside, were equipped with the semi-automatic m1 Garand.
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