Grouping profiles strings having the same words, but occurring out of order
&quot;fuzzy match&quot; is a vague term for many different kind of string similarity measures. There are two main categories:

Sequence-based methods, such as Levenshtein edit distance (and variants), Jaro-Winkler
Bag-of-something methods, such as Cosine-TFIDF, Overlap, Jaccard, ...

Traditionally the first category is used at the level of characters (e.g. to match &quot;abcdefg&quot; with &quot;abdfeg&quot;) and the second at the level of words (e.g. to match &quot;the management of the team&quot; with &quot;the team management&quot;), however there is no technical restrictions to keep it this way. The main difference between the two categories is whether or not they take the order of the units (e.g. words or characters) into account. In fact there are also some hybrid measures such as SoftTFIDF which combine both approaches.
Conclusion:

For the problem of word order, a simple bag-of-words measure such as cosine or Jaccard would perfectly match two profiles.
If more flexibility is needed, Soft-TFIDF or other variants would work.

The last part of the question is about selecting a standard string. In general there's no way to know what should be the standard string from the different variants themselves. A simple approach would be to pick the most common variant.