The countable noun "bread" in English refers to different types of bread.
In Romanian, "pâine" can be an uncountable noun, like in English, but adding an indefinite article before it offers the meaning of "a loaf of bread". The plural "pâini" should be translated as "loaves of bread". I don't think I've heard anyone use "pâini" to mean different types of bread (i.e. breads), we would use "tipuri de pâine".