There's a long vetting process which all studios must undergo in order to get approval to develop on all major consoles. Notice that I use the word: "studios" and this is simply because if you want to self-publish a game you must form an LLC or you won't get anywhere in the application process. (This is where publishers comes in really handy as they already have contacts inside the big 3 and can speed up the entire process.)
If your studio and game project are approved you will receive the game engine licenses of your choice (Unity, Unreal, Game Maker and in some cases special builds which differ from the ones everyone can download online) and will have the opportunity to take a dev kit out on loan. The kits always have to go back at some point and you have to sign a bunch of NDA's basically agreeing that you will never post pics online or allow anyone outside of your studio access to them.
With Microsoft you can actually use any retail Xbox as a dev kit:
https://learn.microsoft.com/en-us/windows/uwp/xbox-apps/devk...
One of Sony's weird requirements is that you must have a static IP address in order to access their dev portal. And I believe that Nintendo actually charges money for their dev kits, but it's been a while since I checked so I don't know if that's still the case.
