Why did it show the "F" when there is no "F" in the 39U, only the "S" which is the same varient and why are both in the MUL if there is only the record sheet for one?
There are two different Thorns that, thanks to in-universe reasons, wind up with the same configuration, though spaced centuries apart. The original Thorn (the -F) has the 2490 date, and is the one that first came off the assembly line. It was later removed from service as upgraded models with Star League tech came along to replace it (the -N). The later Thorn (the -S) is the one ComStar provided to the Combine in the run-up to the War of 3039. By stripping the Star League models of all their advanced tech, ComStar created a "new" model functionally identical to the original -F models that came off the line all those years ago. The MUL preserves the two different entries because, depending on when you're playing and the filters you apply, you're going to be looking for different names.
It is very confusing. Which is the right one,the "F" or the "S"? A;so, since they are presumably the same mech, why have one mech with 2 different numbers? It's just very confusing.
They're both "right", but RS3039 would have it listed as the -S because that's how the mech was known then, and because there were no original -Fs still in existence anywhere. This is a legacy of the fluff, decided many years ago, not a choice on our part - if we were to skip one name, someone else woould wonder what was going on there. There is a Victor with two designations for the same design as well, because the same machine was produced in both the Combine and FedSuns, and was named differently by each - again, years-old fluff forces our hand (and quite frankly, these little hiccups make things a little more "real" to me, so I tend to enjoy the odd one now and again).
The MUL should probably attempt to do something about the -F being listed as appearing in 3039u, since as you mention that exact designation does not appear in that book. I'll see what we can do.