There are bagels...and then there are bagels.
Originally, all bagels were baked in stone ovens, because that's what was available. But over time, things changed. The steel oven came along. That meant that most places in New York moved over to using a steel oven...but in Montreal, stone ovens were still considered superior for baking bagels and continued to be used.
In New York, bagels are baked on burlap planks (i.e. planks that have been soaked and covered in burlap, or sometimes: semolina or cornmeal), something which isn't done elsewhere. Halfway through the baking process, the bagels are flipped over.
There's also something thing about the ingredients in a New York bagel. Back in the early 20th century, the bagel union was formed and members spoke Yiddish and would not share the secret recipe to their bagels.
While some bagel recipes remain closely guarded secrets the ingredients of a New York bagel are wheat flour, yeast, salt, water, and barley malt. Furthermore, barley malt is added to the water the bagel is boiled in.
In contrast, a Montreal style bagel contains less (or no) salt, may have added sugar or honey, and is boiled in water which honey has been added to.
And it's also about that water...in NYC it's soft, in Montreal hard, which leads to a difference in texture in the bagels (or so some experts say, while others hotly disagree).
The Montreal bagel is said to be smaller, thinner, sweeter, and denser. It's also shaped slightly differently with a larger hole in the middle.
Why the hole to begin with? Likely because it was an easy way to boil the dough---you threaded the bagels on a stick, put it across the pot, and then removed it. Unlike a round bun, the interiors are also more evenly cooked (though an oval bun would have the same effect it would be harder to boil without the stick).
Of course, carrying bagels on a stick was also much easier than in a sack if you wanted to peddle them in the streets. With a stick everyone could see your wares.
While on the question of why...why boil the dough? It makes the bread denser and chewier, while the baking in the oven results in a nice crust.
Note that most store bought bagels today have been steamed and are made by machine. Not so in the traditional bagel shops in Montreal and New York. There the bagels are proudly boiled.
You'll find lots of different styles of bagels all around the globe. And did you know that in St. Louis they sometimes slice the bagel eight times vertically...and then somehow manage to stuff it with filling.