Recently I had a batch of unopened 1981-S Proof Sets come into the office. As you know the type 2 version of this proof set is worth over 20 times the price of a regular 1981-S Proof Set. So while I do not suffer from Variety FOMO like some Morgan Collectors I know, I do make it a habit of checking the 1979-S and 1981-S Proof sets that come in. What made these even more interesting was that they were in sealed registered mailboxes directly from the mint. Why does that make it more interesting do you ask? [Even though no-one is asking]. Is that when you get boxes like this from the mint, it is very likely that no matter what you find be it Type 1 or Type 2, the whole box usually winds up the same! So if I open a box, look at the first set and it is a type 2, there is a STRONG probability that the whole box of 5 is the same. This is because these coins are produced in batches. The Type 2 were not some kind of mistake, they were new dies, with a different font used for the mint mark. And they are usually made in the same batch. Not that you cannot get some crossover, but the statistics say all five of the boxes in your order were made at the same time.
As I do with all of my variety checks, and because I am old, and I keep needing stronger and stronger glasses is a review of the 2 types. In the 1979-S I think it is best we call Type 1 Filled, and Type 2 Not filled, with a little serif. Really easy to identify, and you almost do not need a loop. That's big for me thank you. But the 1981-S is a bit tricker. It's a little more nuanced between the types and that's why I wanted to recheck what to look for. I then google it, as well as check the 3rd Party Grading Sites for examples. While there is plenty of information out there, none of it was in an easy side by side so I thought I would do that here. Photos on the left are the Type 1 Cent and Dollar. Photos on the Right is the Type 2 version.
The cent is usually the first place I go since that big fat serif on the top and bottom of the "S" are usually very pronounced.
While on the dollar you can see the Serif is less developed, yet still very much identifiable. Think in terms of the line used to draw the S is either uniform in width, or does the top and the bottom of the S have the bulbous ends. If you have read this far and expected to find out if any of the sets were in fact Type 2. Well, you may just have to wait for that article. :-)
Enjoy.