How to find and delete duplicated photos in two different albums

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What system and Photos versions are you running? Ventura has built in duplicate detection and merges them so only one remains.

If you're using an earlier version then you want an app that will identify the potential duplicates, put them in an album or mark them with a keyword for easy retrieval and deletion by you. You don't want one that does the deletion itself for obvious reasons. 

I've run tests on the these two apps with the following results and found them to be safe to use:

PowerPhotos - $29.95  

PowerPhotos is the iPhoto Library Manager version for Photos and is very powerful. Although more expensive I would recommend it as it has more capabilities than the others like the capability to merge Photos libraries or copy photos, both original and edited versions, along with their metadata between libraries.

PhotoSweeper - $9.99 - Demo version available.

PhotoSweeper compares bitmaps and/or histograms so it can detect duplicate images even if they have different file sizes, file names, image sizes and capture dates.

One photo can be in zero, one, two, or even more albums without being a duplicate. For example, I might add a photo of my friend Billy with his dog Spot at the beach to a "Beaches" album, a "dogs" album, and a "friends" album, but it is still the same photo. Each album just refers to the single photo in the library.

The system-created Duplicates folder is for detecting cases where the same photo exists multiple times in the same library, such as by importing the photo twice.

All that said, I haven't answered your question about how to detect a photo that appears in two different albums you name. There is a way, if you are comfortable creating a Smart Album. Use the "match all" combiner and two "Album" "is" conditions", as shown below: