The pretzel originates in Germany, where it is called Laugenbrezel. It was originally prepared in a alkali solution, which is where the "Laugen" part of the word comes from; typically, lye was used, but baking soda gets you most of the way there without a trip to the pharmacy (a Mexican or Asian market may do the trick if you want culinary lye).
The alkali solution is what causes the crust to brown so deeply, and it's most of the difference between a pretzel and a bagel. A bagel would typically be boiled in a malted sugar solution instead. The flavor is also affected, but I don't know how to describe the difference; there's a very pronounced aroma difference if you skip this step. To me, you end up with nothing more than a pretty breadstick unless the dough gets that alkali bath.
If you do use culinary lye, use gloves and don't rush anything. Traditional Laugen aren't boiled, so you just need a cool 3% lye solution; no boiling step.
In Germany, the pretzel shape isn't the only option for Laugen. Little rolls calls Laugenbrötchen and longer, roughly baguette-width sticks called Laugenstangen are also popular. On my most recent trip last year, the Laugenstangen were frequently sold in the form of sandwiches, though I don't remember seeing many of those when I was first living there in the mid-90s.
ETA: Having done this a few more times since originally posting, I'd also add that the utensils you use in lye-based pretzels need to be wood, glass or plastic. Eye protection is important too. Metal will likely corrode or oxidize when it contacts food put in contact with lye, even if it's after the wash. I'd recommend setting the washed pretzels on a wooden surface after dipping if you want to minimize damage/discoloration on your baking sheet.