Modes are even more foundational to Emacs than to Vim. A new user will encounter a dozen modes by simply starting to use Emacs for a few minutes. Every buffer has a major mode, and there can be many minor modes enabled per buffer or globally. The entire editor is built on a tree of modes, all inheriting from the aptly named Fundamental Mode.

At a basic level, each mode affects what every key does. The idea of keys doing different things in different modes is not unique to Vim.

Which just goes to show that Vim's definition of "modal" is somewhat contrived, as Vim's definition of "modal" applies to a very specific implementation of two to four modes (which coincidentally Emacs also offers multiple versions of, both natively and as third party packages to varying degrees of faithfulness).