Thin 2D stamp:
Then, as again mentioned by @cullers , Thin stamps were printed on Holo Base Set cards, which later also became the standard for the next sets. The “1” in this Thin stamp is thinner than the Thick stamps, and the “EDITION” is also thicker. (This also causes some controversy / discussion about the name Thin stamp, and a lot of people think the Thin and Thick stamps should refer to the stamp itself rather than the width of the “1”, which would mean the terms should be swapped. But, it is what it is, and these are known as Thin stamps.
Originally the names were most likely called “Thick one stamp” and “Thin one stamp”, but over time the “one” part has been removed, leaving the confusing terms we have today when we talk about the stamps.
There are also a select few Thin stamps on non-holo Base Set cards. These are extremely hard to find, and almost non-existence. Because their numbers are so low, they either only made one or two printing sheets with these non-holo Thin stamped cards, or it’s a printing-misprint instead (like the Thin Grey stamps we’ll cover later in this article). Here is a picture of a Thin Stamp on a non-holo card as example, and some more can be found in @acebren 's collection thread.
Thin 3D stamp:
A Thin stamp Base Pikachu was shown on the forum by @cinnaminhbun . This card was not only a (borderline) Thin stamp, but also a 3D stamp.
(Here a link to the full picture.)One thing to note is that this non-Holo Thin stamp is not as Thin as a Thin Holo stamp. It’s definitely thinner than a regular Thick stamp, but more in between the Holo Thin stamp and Thick stamp variants. Here a comparison picture of a Holo Thin stamp, this 3D Thin stamp, and a regular Thick stamp:
Smudged Thin stamp:
In some cases a stamp can be smudged. It may not really be an actual variation, since it’s misprinted, but I still think it’s worth mentioning here, considering most of these stamp variations are misprints to begin with.
Here a Smudges Thin stamp that was found on a Red Cheeks Pikachu by @megacon :
(Here again a comparison picture with a Thick stamp. And an addition comparison picture with a Holo Thin stamp, to see they don’t different in width that much.)
And when a stamp that was already Thin gets smudged, there is almost no “1” left… Here an example of such a stamp on a Holo Gyarados from @shizzlemetimbers ’ collection:
(And here a comparison picture with a regular Thin stamp Gyarados.)