Why do we say languages such as C are top-down while OOP languages like Java or C++ are bottom-up? Does this classification have any importance in software development?
It's more about paradigm (object oriented, imperative, functionnal etc.) than syntax.
From dept-info.labri.fr
Bottom-up programming is the opposite of top-down programming. It refers to a style of programming where an application is constructed starting with existing primitives of the programming language, and constructing gradually more and more complicated features, until the all of the application has been written.
Later in the same article :
In a language such as C or Java, bottom-up programming takes the form of constructing abstract data types from primitives of the language or from existing abstract data types.