Is "Inbox" the old stock email application?
No. Inbox is a very different application that was opened to the public in early 2015. It's primarily designed around the idea that your inbox is like a to-do list of sorts. The project's website explains this in more detail.

The "Android" email application is no longer developed by Google in any meaningful capacity, aside from ensuring that new platform releases do not break the build (and some translation updates, which are mostly automated). The Exchange and IMAP/POP features were instead rolled into Gmail, which is now considered the "stock" email application on any Google device.