Way too complicated.When you have a lot of something, you need words to describe different kinds.
So chickens, ducks, and geese are kinds of birds.
Rocks and Wyandottes and Leghorns are kinds of chickens.
Barred Rock and White Rock are kinds of Rocks.
Or shirts and pants are kind of clothing.
Jeans and sweatpants are kinds of pants.
T-shirt and sweatshirt and polo shirt are kinds of shirts.
Northerners need ways to describe different kinds of coat, so we have puffer and windbreaker and parka and so on.
Many kinds of "coat" can also be jackets, but not all of them. Jackets are not ankle-length (like a trench coat), and jackets are more likely to be light in weight (summer jacket vs. winter coat.)
Of the terms in the poll, I've never heard of "warmer" being used to describe such a garment, but it might be common in another part of the country. I've encountered all the other terms you list.
I would typically use "coat" for all the things in the pictures, "windbreaker" for a different style of thing, "jacket" as a synonym for windbreaker, and "puffer" only if I had to distinguish that particular kind of coat from some other kind. The white one in the picture is not a "puffer," but I don't have a special word for that style of coat.



