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Maybe I'm being a bit simplistic, but there is only one string where the letters obviously and simply follow the instruction. I hope I'm right. I usually find with these crosswords that the solutions are simpler than they might at first appear.
By the way, nowhere are we ever told that we should refer to Wikipedia, and I usually find, when general knowledge fails, that any necessary information can be found with the briefest of internet searches.

Maybe I'm being dim, but why do 2 and 6 not both meet the requirements?

Maybe we’re at cross purposes, sh. But in lower case does the first letter of the second string not undergo the second part of the instruction to become the second letter (without tail)? Mind, I don’t have a maths degree from Cambridge!

If you look on an individual letter basis, yes, I agree, and I guess that's what you're supposed to do.

But the preamble says the set B instructions describe one of the strings. Each string has 4 letters. And if I look at the strings as single units of 4 letters, both 2 and 6 can be rotated to get back to the same thing, and cannot be reflected to get back to the same thing (as far as I can see). So to me both strings meet the requirements as set out in the set B instructions.

But I can now see that if you look at the generation process for each string, one works and the other doesn't. So I guess it's ok. But a bit loose in my view.

I don’t necessarily disagree, sh. I chose to interpret string as a succession of operations, rather than an individual one, because it was the only way I could differentiate a unique solution that satisfied the instruction.

String 2 can be reflected to get back to the same thing. It requires 2 reflections, one perpendicular to the other.

Same thing works for string 6 doesn't it? If you're allowing multiple reflections then no string passes?

I hope this is not giving away too much but it is late in the week. I
see it as a series of operations. String 2 is reflect rotate reflect.
String 6 is rotate rotate rotate.
String 4 could be anything as you can’t tell if the letters have rotated, reflected or neither but if you accept that each string is different it is not the correct answer.
I considered if it is sufficient to rewrite the correct string above the grid or if you need to create or reproduce a design which fulfils the criteria. I suspect the latter or there would really be no point in adding that element.

If we consider how one letter becomes the next, there is only one string that clearly satisfies the instruction. We can discount string 4 as it is not clear how it is generated.
String 2 is unusual because, unlike the others, it cannot be considered as a repeated pair of transformed letters. If it is considered as being a string of four different letters generated from a single letter, it does not follow the instruction. As a string of four letters, it does not demonstrate repetition of the whole pattern, as one would expect in a frieze, and it provides no evidence to suggest how it would repeat. Considering the string as a transformation of a pair of letters would meet the criteria, but to apply the same consideration to the other strings would reduce them all to translations, in which case, any letters of the alphabet could have been used.
There is no reason to suppose that all the strings should be of a different type. Strings 7 and 8 are both translations.

7 and 8 could be different though. 8 may involve a horizontal reflection whilst 7 cannot.