Terminal emulator is the window, the tabs, integration with your desktop, etc.
Shell is more complicated but TLDR is this is everything showing in your terminal window by default, the base program you use that runs other programs. The prompt showing current user, saving history, coloring the input, basic editing keyboard shortcuts, etc.

By having this AI integrations in a terminal emulator we are very much limiting ourselfs. It would look more fancy in popup windows, but it won’t work over remote connections and not be as portable.
Usually when we do some smart functions like autocomplete, fuzzy search or integrations like that we do it as an shell (fish, bash, zsh) extension, then it will work on any emulator and even without a GUI.