Ok look, the Xbox one or ps4 (any console now days) occasionally receive updates for their OS (operating system) which add features, improvements, etc. And of course that requires internet and memory space for that. All consoles now days have a hard drive where they install everything from games to OS or game patches. On the Xbox side games today also are sold digitally from the Xbox store or physical like you already know. If you buy the game physically when you first enter the disc it installs the full game on the console's hard drive and the disc must be in it to play it, otherwise its gonna ask for it to start the game. If you buy it digital obviously it installs itself on the hard drive too and you can play it like instantly. The Xbox one console have two Power modes you can select to turn it off: A full shutdown mode called energy saving where it's totally off and a instant on mode where it goes to sleep and it turns on quicker and almost all the game / updates are installed automatically. If a publisher releases a patch update for a game it'll download itself automatically while you aren't using the console, same applies to console OS updates, unless they need some sort of input by the user. Gone are the days of Xbox 360 where you had to turn on the console to update and stay a game to be surprised with an update patch. In my case I've never had to deal with any updates at all except for a game called warframe which requires user input to continue. Other than that, if you put the power mode on instant on, you have to deal with any updates and stuff.
Now about game formats. Me personally choose on this console digitally and haven't bought a game disc. Only one I have is mortal combat X because it came with the console. I like the convenience that you can start the game without getting out of the couch to switch discs {your laziness mileage may vary
}And if it's going to occupy the same hard drive space still well, better digitally. Only con is that usually you get the discs cheaper on eBay or Amazon, but can also get cheap digital games. As far as I know, the ps4 play games from disc, installing textures and stuff is optional, or you can buy then digital too. Dunno about updates since I don't own one.
If you're worried about hard drive space, aside from the one included inside the Xbox (which you can't upgrade officially) you can use any usb 3.0 hard drive larger than 256GB as a external memory. My recommendation would be to buy the one with the biggest hard drive from the beginning if you can ($$$). Right now options are 500GB, 1TB and 2 TB. Unless the deal is So awesome for a 500GB one or something like that, I would go with the 2TB one. Enjoy!!
Aaaaand to answer your question, OS patches and game patches vary from size, a game patch can be 700mb download or 7GB download, depending on the content included, same applies for os updates, which usually don't are more than 800mb as a maximum
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