I read a headline on a genealogy search site that read “spelling doesn’t count.” While it’s true that your ancestor’s names may have not have been spelled precisely the “correct” way and the same way every time, spelling does count–to a point.
It’s not the precision of the exact letter match that is important, it’s the sounds suggested by these letters that matters, at least partially. Trautvetter, Troutfetter, and Trautbetter are not spelled exactly the same but the sounds represented by the different letters are similar enough that the spellings likely refer to the same “name.” There are other factors at play as well. Handwriting issues, Trautveller for Trautvetter, vowels misread as consonants, Trantfetter for Trautfetter, and similar challenges are also concerns.
And there’s always Wharton being rendered as Horton. Sounds are important.
It’s probably a safer bet to say that spellings don’t have to match exactly.