Pretzels most likely originated among monasteries in Europe, and their distinct shape is said to represent hands in prayer. Then in the 18th Century, German and Swiss immigrants introduced them to the US, and it soon became part of their cuisine.
Anyway. There doesn't seem to be much literature online on the differences between American and German pretzels, but by looking at different recipes, I've found that:
1. American recipes usually ask for all purpose flour, i.e. low gluten flour, whereas German pretzel recipes ask for bread flour.
2. American recipes say it's fine to just dunk the pretzels in a bicarbonate of soda solution water before baking, but the German ones strongly recommend the sodium hydroxide that's actually quite difficult to acquire.