All the JC Higgens shotguns I've seen were made by High Standard. The only Sears firearm that Winchester made was the model 54, a lever action rifle. Savage/Stevens made most Wards shotguns, Winchester apparently didn't make any of those either.
I had a 20 ga JC Higgens, and my Dad had a 12 gauge. They were both High Standards and I've handled the equivalent High Standard Models.
My Nephew had a Sears shotgun made by Winchester. It was identical to the model 1300 except the impressed checkering had a different pattern.
I don’t remember if it was marked J.C. Higgins or not. It was actually a pretty good looking gun with a very high quality blueing. I never liked impressed checkering but other than that it was nice.
I only made the comment as my “Ted Williams” was made by Winchester. I actually preferred it as it had nice walnut furniture. Good guns.