Rear Seam (early):
This is the same design the US used in WW1. It is cut slim so it tightly fits around the metal canteen set, making it harder to use than later versions. The rear seam style was only produced in early 1941 (source: https://www.usmilitariaforum.com/forums/index.php?/topic/290799-m1910-canteen-cover-rare-manufacturer/) at Baker Lockwood, though some 1942 dated examples have been found from other manufacturers like Jeff QMD (JQMD, source: https://www.usmilitariaforum.com/forums/index.php?/topic/290276-oddjqmd-1942-canteen-cover/, https://www.usmilitariaforum.com/forums/index.php?/topic/198250-the-last-of-the-realm1910-canteen-covers/ ).
Sides and Bottom:
Side Seam (later):
Most US Army WW2 canteen covers are this version since it was easier for soldiers to use because it was cut to make sure it does not grip the canteen set as tightly as the rear seam version above. This also allows room for the material to shrink since soldiers were told to wet the canteen covers in order to help keep the contents cool (source: https://olive-drab.com/od_soldiers_gear_canteen_carrier_cotton.php), which would naturally cause shrinkage over time.
Sides and Bottom:
Wool lining for insulation.
This particular example is also dated to 1941 and was produced by the same manufacturer, Baker-Lockwood, as the rear seam one above. The side seam pattern was officially authorized in 1942 (source: https://history.army.mil/html/museums/messkits/Field_Mess_Gear.pdf), though some manufacturers continued to make the old rear seam pattern into 1942 (source: https://www.usmilitariaforum.com/forums/index.php?/topic/290276-oddjqmd-1942-canteen-cover/, https://www.usmilitariaforum.com/forums/index.php?/topic/198250-the-last-of-the-realm1910-canteen-covers/).