Your shell is from the same period as the gun, but is probably a 3-inch case. Actually old Researcher is thin on early Winchester ammunition paper. I'm much better with UMC & Rem-UMC, and Western.
That primer is likely the "New No. 4" --
which was in use from around 1904 until after WW-I. Winchester shotgun shells sold factory loaded had WINCHESTER on the headstamp, and those sold as NPEs had 1901, again until a bit after WW-I. The earlier primer would have been the No. 4 --
