Where is the terminal application on the filesystem?

Is this all you want?

/Applications/Utilities/Terminal.app

In macOS 10.15 Catalina, I found it in:

/System/Applications/Utilities/Terminal.app

This is how I found it:

1. open Spotlight (Cmd+Space)
2. type: Terminal (typing the full name ensures it's the first search result at the top)
3. if not already selected, select (single-click) the Terminal.app found by Spotlight (should the first one in the list), after the app is selected, press the Cmd key, while holding that key the full path will be shown in the bottom-right corner of Spotlight
4. alternatively continue with the following steps: hold the Cmd key, then hit the Enter key or double-click on the Terminal.app found by Spotlight
5. that will open Finder and highlight Terminal.app
6. if you drag Terminal.app into a text file, another terminal, or even a browser URL bar, it will show you the full path

(Funny enough, if you right-click and choose Get Info, it will show you as if it's actually just in /Applications/Utilities, e.g. without /System).

The difference between the two paths is significant when used in a shell or (I assume) programmatically, for example:

~ % file /Applications/Utilities/Terminal.app
/Applications/Utilities/Terminal.app: cannot open '/Applications/Utilities/Terminal.app' (No such file or directory)
~ %
~ % file /System/Applications/Utilities/Terminal.app
/System/Applications/Utilities/Terminal.app: directory