When you download the store version of Vim (specifically GVim or MacVim), you unlock features that the standard terminal version sometimes lacks:

Easier rendering of specialized coding fonts like Fira Code or JetBrains Mono. Is the "Store App" Different from the Terminal?

Run sudo snap install vim-editor to get a containerized version.

Easily copy and paste between Vim and your browser.

Essentially, no. Whether you download it from a store or a terminal, the core engine is the same. The store app usually just adds a "GUI wrapper" (GVim) around the engine. You still use :w to save, :q to quit, and i to enter Insert Mode.