So according to Merriam Webster bread is:
a usually baked and leavened food made of a mixture whose basic constituent is flour or meal
And cake is:
A: a breadlike food made from a dough or batter that is usually fried or baked in small flat shapes and is often unleavened
B: a sweet baked food made from a dough or thick batter usually containing flour and sugar and often shortening, eggs, and a raising agent (such as baking powder)
And yet some people don't think that cake is bread.
I once had a similar thought and reached the conclusion that based on dictionary definitions, everything can be categorized as either a soup or a salad.
Cake and bread are actually the same since they are both soups.