relationship of Pictures on Mac to the Photos app

The Photos.app has to be in the Applications folder, like all applications installed by the system.

The Photos Library created by Photos will appear in the Pictures folder, unless you move it somewhere else. You could move it to an external drive, if you want to save storage on your Mac.

A Photos Library is showing an icon with a stack of three pictures with the rainbow flower, like this:

The photos.app is having an icon with a single image of the flower.

The Photos.app on your iPhone is showing you all photos that have been saved to Photos. The Camera.app is automatically saving new photos in Photos, but you may also have photos stored by the Files.app outside the photos Library. On the Mac we can download photos directly from a camera into Photos as well.

To elaborate a bit on what mugay summarised:

• The Photos.app is a is a combination of a digital asset manager (DAM) and a photo editor. All photos are stored and managed in a database, called the Photos Library. The Photos Library is a closed package. We do not see the media managed by Photos in the Finder, only the Photos Library. We can have have more than one Photos Libraries.
• The Pictures folder is the default location provided by macOS where we are invited to store our photos, that are not managed by Photos. Many image editors will look first in the Pictures folder for photos. It is also a good place to keep our Photos Libraries there.

Perhaps you have expected the Photos.app to be more like Picasa or other DAMs, that create a catalogue for the photos we are storing in folders in the Finder and are just referencing the photos in their original location.

You could use Photos this way, but it is currently a bit buggy and not well supported. I cannot recommend to use Photos with a referenced library, until Apple adds a better support for this.

The pictures folder is where most users keep their photos library (although you could put it anywhere). Your actual pictures are kept within the library and are accessible using the Photos app.

If you have iCloud enabled, any image you add to your photo library will upload to iCloud.