Bach's Gavottes

In listening to pieces from my Classical Music Queue (explained here), I recently listened to Bach's partitas for solo violin.  Or at least I listened to what excerpts I have; I have complete recordings of the first and third, but only one movement from the second.  In listening to the gavotte en rondeau of the third partita, I found a similarity to the gavotte in Bach's third orchestral suite:

(notation found here and here)

There are three groups of trills (with the first two notes as eighth notes and the third as a quarter note), and while the note groups of the two works aren't in the same intervals, the general position pitch-wise is the same.  That is: in both works, the first group of notes is the highest; the second is the lowest; and the third is in between the first two.  Both are capped with a (relatively) lower half-note.

There are a lot of threes here - the number of notes in each group, the number of groups, the movement number, and the classification number (No. 3).  Apparently, Bach didn't put the suites in a set though, so the "No. 3" part of "Suite No. 3" is just a coincidence.

In researching the pieces, I haven't found any dates of composition that agree with each other (the partita seems to be 1720, but I've found both 1717 and 1730 for the third orchestral suite), so I can't tell whether the partita or the orchestral suite was written first.

When I add a piece to the Classical Music Queue, I also write down where I found a reference to it.  Interestingly, the partitas were mentioned in some interviews given during a performance of all four of the orchestral suites that I listened to on NPR in November.  However, neither of the times it was mentioned was really a comparison between the partitas and the orchestral suites.