Frankly the “Brazil style” sounds fake. Dunno if someone out there eats it this way, but it’s a lot like trying to pretend that the Guatemala, New York and Sonora styles are the same “North American style”. For example, where I live in Paraná, I’ve seen at least three types - none including carrots or cilantro*.

Street “podrão” (big rotten):

• Usually includes a secondary meat. Beef cubes, ground meat, shredded chicken, stuff like this.
• Potato mash, fried yucca meal, or both.
• Some creamy cheese, not just Parmesan. Usually requeijão.
• If the hot dog is opening that way, something is wrong. You’re supposed to press the whole thing on a hot plate, until it’s roughly brick-shaped. It’s easier to eat and the bun is slightly toasted.
• Salmonella is a seasoning! (Food poisoning is a concern.)
• Pico de gallo is by no means obligatory. It’s fairly common to sub it with sliced cooked onions instead. I’ve seen a few with sauerkraut too.

Vininha: basically pigs on a blanket: the wiener is cut in half, then covered with dough, and then baked. Kids love that stuff.

Pão com vina: homemade. The wieners are chopped and heated on a thick tomato sauce (the same sort that you’d add to pasta or pizza) and served/eaten inside a “water bread”* (pão d’água) or “French bread” (pão francês) bun, alongside the seasoning of your choice. Pickles or sauerkraut are fairly common.

*I don’t rule out the possibility that someone out there does it this way, mind you, my point is that it’s a damn weird generalisation.

**it gets this name because the bread is baked in a high moisture environment.