Finding photos on your phone 'should' be a relatively simple task, but unfortunately it's become an increasingly and unnecessary problem, for all of us. At one time, years ago, a standard folder was designated by default as the central storage place for image files. A DCIM folder (Digital Camera IMages) was used for phones, tablets, web cams, hand-held cameras, other mobile devices, etc. If an image file was involved, it would be retained in the DCIM folder of that device.
But now it's a much more a mixed bag of possibilities -- the default folder to store your photo files might still be the DCIM folder, or it might instead be named Photos, or Pics, or Images, or whatever, depending on the whims of whichever manufacturer of your phone model and how they chose to set up your phone's internal file system arrangement. So your phone's Camera app might still be using the DCIM folder as its default save location but your text messaging app and your web browser app will likely be using the Downloads folder for its default save location. So the bottom line is there are likely going to be multiple folders where your photo files are being stored, which adds another layer of complications.
In your posting note that there isn't a 'Gallery' folder that stores its own photo files. The Gallery app is just an image viewer/editor. It only displays the existing photo files that are stored in whatever folders the app can detect. And that's the weak point, the Gallery app doesn't have the ability to detect and index every photo file stored within your phone's internal storage media,nor microSD card. It will only scan for photos in predetermined folders. So if you also have some photo editing app installed that uses its own app folder to store images done by the app, those photos won't be automatically displayed when you start up the Gallery app. The same issue applies to the Google Photos app, it's also a image viewer/editor that scans for photos stored in some but not all folders.
In essence, when it comes to where your photos are stored on your particular phone don't look at the apps, you need to determine which folders are used to store photo files by the apps you use. Use a file manager app to actually manage your photo files/folders, use a photo manager app (ii.e. the Gallery app) to view your photos.
What phone model you have? Samsung phones come with a basic file manager app named My Files, It has a limited feature set but if all you need is the ability to do basic tasks like copy, move, or delete files and folders it may be all you need. Otherwise, your phone may already have a file manager app pre-installed or there are a number of really good ones in the Play Store. For more involved tasks like remote networking you might find the Solid Explorer app a better option (especially with pay-for addons). It's a feature-rich file manager that's also very user configurable.
https://play.google.com/store/apps/details?id=pl.solidexplorer2&hl=en_US&gl=US&pli=1
Simple Mobile Tools has a file manager that's Open Source (no ties to any business oversight) and comes with a nice user interface.
https://play.google.com/store/apps/details?id=com.simplemobiletools.filemanager.pro&hl=en_US&gl=US
There are a lot of other completely free file manager apps to choose too though. Go to the Play Store, search for
file manager, and look through the posted screen shots for each to find the one you'd feel most comfortable using.
