There are some fundamental aspects to your photo library that you need to take into consideration so you don't let some misconceptions mess up how to manage all your photos.
-- When you use the Camera app on your phone to take a picture, the app saves that photo to a file stored within a specific folder in your phone's internal storage. Take a bunch of photos and you of course end up building up a sizable photo library. But there's an added twist to complicate things. Your friends and family probably have sent you a lot of photos via email and texting. Plus you might be saving some photo files using your web browser. While it would be nice if all those photos would end up in the same folder but that's just not the case. While most email apps, most texting apps, and most web browser apps use the Downloads folder as their default save folder, and your Camera app uses it's specific default save folder (varies by name depending on the manufacturer so could be DCIM (Digital Camera IMages), or Photos, or Pics, or whatever), that's not always the case as some apps use their own default save folder. So there are a lot of variables involved based on your phone model, Android version it's running, which apps are involved, etc. as far as just where your photo files are stored in your phone.
-- Regarding the Gallery app and the Google Photos app, both are just photo display apps. They automatically scan, detect, and index your phone's internal storage for photo files, then when you start one or the other up it pops up on your display showing your photo library in thumbnail images in a cutesy way. They're just viewers, so you're not actually storing any photo within one or the other. That's a big distinction to keep in mind -- your photos are actual files stored in different locations in your phone's storage media. (... with a side issue being one or the other might have better capabilities in detecting all those different folders that may or may not contain photo files.)
-- A significant feature that the Google Photos app includes that the Gallery app does not is that Backup & sync function. This also involves a number of other twists and managing your photo library as a whole. If you just rely upon the default settings of the Google Photos app things swing in one direction. But if you customize/optimize some of those same settings, things swing in a different direction. So if you're trying to get a good grip on managing all your photos files in a way that best serve your own particular needs be sure to look in the Google Photo app's 'Photo settings' menu and pay close attention to which options do what function so you can configure things accordingly.
-- Ideally it would be best to have your entire photo library on your phone and an exact duplicate backed up safely and automatically so any changes on your phone or to the backup are also done automatically and concurrently. In this scenario, you can view all your photos on your phone, or via a web browser to view the exact same thing stored in your backup. Both photo libraries are constantly being synced with each other in the background.
But there are some options in the Google Photos app that can alter this setup in order to free up storage space in your phone's internal storage and/or free up storage space in your online Google account (that's what the Google Photos app uses as its default save location, in your Google account storage. If you go to the Google Photos app >> Photo settings >> Back up & sync menu there's a 'Upload size' option. You can choose to have your backed up photo files left as is or have them automatically scaled down to a lower resolution to cut back file sizes. At this point your phone's photos will be left as is at their original, higher res while your online backed up photos will a slightly lower res. Or to free up more storage space in your phone, use the 'Free up device storage' option. This will remove photo files from your phone when they get backed up into your online Google account storage. Personally If find this particular option to be a bit abhorrent -- this requires your phone to always have an online connection (either WiFi or mobile) to have actual physical access to your entire photo library because some of your photos will be on your phone and some only when you can access them online. While you do have the thumbnail images to peruse through using the Google Photos app, it's hardly optimal if you want to do something to the actual photo file. And the Gallery app is only going to be able to access those files that are on your phone. But there are those who have limited storage space in their phones and have built up a large number of photos so there is that.
So set up the Google Photos app with some thought as to how you want to manage your own photo collections, and don't forge to keep in mind there are going to be two different but identical (maybe) photo libraries. One being your on your phone (in different folders and accessible via the Google Photos app) and the other being within your online Google account (accessible using a web browser viewing
https://photos.google.com )
