Post History

I don't hear much of a resemblance. If nothing else, the W. F. Bach is in quadruple time, while the J. S. Bach is in triple time. 

But to answer your broader question: Copying motifs and tunes from other composers was widely accepted in the Baroque era and even later. Music at the time was written for an occasion and then replaced with new music. Old "intellectual property" had little value.

A well-known example is the chorale often known in English as "O Sacred Head, Now Wounded." The author of the tune was Hans Leo Hassler. J. S. Bach used it in his St. Matthew Passion, using different words and his own choral harmony. The tune is often misattributed to Bach today.

In the Renaissance period, the use of existing tunes in settings of the Mass was widely accepted. They're often called "parody masses," even though they aren't parodies in the sense of satirizing anything; they were serious and accepted works. 

Some works in the Classical era were initially misattributed because they were reworkings, often with just minor changes, of other composers' works. The work formerly called Mozart's Symphony No. 37 was actually Michael Haydn's Symphony No. 25, with a new introduction and perhaps some other minor changes by Mozart.

Composers sometimes reused their own works. Rossini's well-known overture to _The Barber of Seville_ is almost identical to the overture to his nearly forgotten _Elizabeth, Queen of England_. Beethoven took large chunks from his early _Cantata on the Death of Joseph II_, which wasn't performed because he missed the deadline, and worked them into his opera _Fidelio_.