You've just reminded me of a German colleague who moved to the US that was asked in his first week "How are you enjoying things? What have you found surprising?" and replied with "Shopping has been difficult because I don't recognise most of the brands or products. The supermarket has like 100 different types of bread, except as best I can tell it's actually just the 1 type of bread in 100 different shapes. Also it's not bread, it's more like a cake."
I mean it's the same in the UK - there are probably 30+ different types of bread in any supermarket, but it's all the same. It has the same shape, same taste, just different bakery that makes it.
I'd say the UK is somewhere in between, with different types of white bread actually being different (e.g., baps vs rolls). My early encounters in the US were similar to my German colleague where much of the variation in bread was simply to shape (e.g., rolls vs sliced loaf) but it was ultimately the same flavour and texture. Obviously in both countries you can go looking and find a much broader array of options. It's just a stark contrast to experiences in many continental European countries where almost any store that sells bread seems to have white, sourdough, regular rye, dark rye, etc. and each variety is so vastly different in taste and texture.