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?
I've never heard the terms "top-down" and "bottom-up" used in that way.
The terms are usually used to describe how one approaches design and implementation of a software system and so apply to any language or programming paradigm.
In "On LISP", Paul Graham uses the term "bottom-up" slightly differently to mean continually extracting common functionality into shared functions so that you end up creating a new, higher level dialect of LISP that lets you program in terms of your application domain. That's not a common use of the term. These days we would call that "refactoring" and "domain-specific embedded languages" (and old LISP programmers would sneer that LISP has been able to do that since the 1950s).