Photos works, roughly, on a database model.
If you're on the iPhone, it wants to keep your photos in the Camera Roll. Think of the Camera Roll as a special area that is not visible to Files, but that is visible to apps that have been specifically programmed to use the Camera Roll and that you have given permission to access it.
If you're on the Mac, it wants to keep your photos in the Photos Library. (There's an option to store originals outside of the Photos Library, but Photos is still going to need the Photos Library to track things and to store edited files. You can't use that option if you have iCloud Photos turned on, so let's ignore it for now.)
The Mac version of Photos is more open than the iPhone version, inasmuch as you can Export (File/Export…) copies of your photos to any place to which you have write access, and do what you please with those copies.
With the Mac version of Photos, if you want to use another editing program, you can often run it from Photos. That allows the other program to save changes directly back to the Photos database (even if the people who developed Photos don't want you messing around in that database and possibly breaking things).
On the iPhone, you would run another editing app that was Camera-Roll-aware.
If you use iCloud Photos, then all of your Macs, iPhones, and iPads which have iCloud Photos turned on, and that are connected to the same iCloud/AppleID account, will upload new original photos as soon as they get a chance. Each device will try to synchronize its Camera Roll (iPhone, iPad) or system Photo Libary (Mac) with what it sees as the master copy of your photo database, stored in iCloud, on Apple's servers.
Take a photo on your iPhone and it will show up on your Mac. Import a picture from a regular digital camera into your Mac's system Photos Library and it will show up on your iPhone.
iCloud IS the "mother ship" as far as the master copies of the photos are concerned.
You can set up your devices so that they will throw away full-resolution local copies of photos if they start running out of storage space. I've set preferences on my iPhone so that it can throw away full-resolution local copies, and set preferences on my Mac (which has much more storage space) so that it can't.