In effect both designations may be correct, depending on the type of pretzel(l) targeted. In general, a distinction is made between the Swabian variant and the Bavarian variant.
In the Swabian “pretzel” the small arms are rather thin and the pretzel belly is incised on the surface. Their fat content is 3 to 10 percent.
them bavarian “pretzel” has big arms, a torn surface on the belly instead of the cut, and a fat content of less than 3%.
Incidentally, the Bavarian variant was entered in the European register of typical regional specialties in 2014 under the terms “Bayerische Breze”, “Bayerische Brez’n” and also “Bayerische Brezel” and has therefore been an EU protected designation ever since.