I know there are questions here already about Quick bread vs cake, or muffins vs cupcakes. But I'm not asking about the sugar, fat ratio thing. I'm more interested in the "bread" part of it. To me whether it is American white bread, or Italian or French bread, it is a sugarless loaf used to make a sandwich. Even biscuits and rolls that can be made with baking powder instead of yeast can be used for breakfast or lunch sandwiches with sausage and eggs. But you can't make a sandwich with banana or pumpkin bread, you treat them as a cake. so why "bread"?
Cooking terminology is vague and has evolved to suit the avilable ingredients in various places at various times. This means that the categories are not clearly defined. Here are some examples to indicate the continuum between bread and cake.
But teacakes are bread, in that they're yeast-based. Not all have much sugar in the dough, though the recipe I've linked does. Chelsea buns are an unsweetened yeast dough with a sweet filling rolled and baked in.
Brioche is undoubtedly a bread (yeast), but is often sweet.
There are many different types of classification, and you can't use classical classification for most things, especially when the concepts have been around for a long time, and spans multiple cultures.
What often happens when two cultures have similar things is that to explain the concept more easily to their culture, a group will explain the concept in terms their culture will understand. So you come across a leavened, wheat-based baked product, it's a 'bread'. You may later add a qualifier to differentiate if the cultures mix (eg, 'yeast bread' vs. 'soda bread').
With classical categorization, you come up with defining characteristics of the group, and anything that matches is in the group, while things that don't aren't. This was my setup for my question about types of pancakes, and the resulting demonstration and presentations
The problem is, everyone can come up with their own defining characteristics -- people wouldn't have cared about defining bread by sandwich-making in the centuries before sandwiches were invented.
Most categories that aren't strictly defined for some specific purpose are defined by prototypes -- you may have a 'protypical' item, and you judge the categories by how close things are to the prototypical items. So penguins and ostriches are birds, even if they're not the first things that most people think of when you say 'bird'.
And in this sense, soda breads are breads. So are muffins. So are most cooked starch items that you can toast.
The problem comes as what you select as your categories that you're sorting things into. Is cake is own category, or a sub-type of bread? Well, that probably depends on why you're sorting things.
So, if you're really interested in 'sandwich breads', then you might consider things differently. Cake won't make a good sandwich, but tortillas would. But would everyone consider tortillas to be 'bread'?
If this sort of thing interests you, see if your library has/can get George Lakoff's Women, Fire, and Dangerous Things