Morphological differences are associated with a chromosomal difference.
In tan-striped birds, both copies of chromosome number 2 (the second-largest chromosome) are acrocentric (shaped like a clothespin).  In white-striped birds, one copy of chromosome 2 is acrocentric and the other is metacentric (shaped like a letter X).  This is due to a structural rearrangement (a pericentric inversion) of one copy of the chromosome:  two breaks have occurred in the chromosome, the center piece has been turned upside-down, and the pieces have joined back together.  (Photos were shown at the DVOC meeting.)