Thanks for the link to my article, @acebren . 
@mikejofthecoast It looks like a nice variation in your side-by-side comparisons. I didn’t even knew it occurred more often. I’ve heard it sometimes occurred with Team Rockets cards, but never seen them side-by-side like that. TIL. I agree with @azulryu that it’s worthy of its own variation, so I will add them to my article soon and send a reminder to myself right now. I personally see the “thinner” variation as smudged personally. With all of the ones you’ve posted pictures of you also see a black halve circle striking through the “EDITION” in your pictures. It’s not as bad as this Dark Gyarados from @shizzlemetimbers 's collection though, which I would see as an actual Smudge error, since also the entire “1” is covered in ink.
But to answer your original question: only the Base Set contains Thick 1st edition stamps (wide “1”); all other sets only contain Thin stamps (thin “1”), and variations of those (like the Grey Thin stamps, these or worse Smudged Thin stamps, and the “d” edition Butterfree printing bubble).
Greetz,
Quuador