I'm using the photos app on my mac as well as on my iphone/ipad. Is it possible and if so how, to move pictures into a album in a way that is not shown anymore under "all photos"?
You cannot move image files within the Photos.app.
You can link the image files to albums, or use 'smart albums' to filter the image files.
If you want to move them like files in a file system you will need to ditch photos.app and use a different application on the Mac, or go with a directory structure in the file system. On the iPhone/iPad it will be a bit more complicated, as there is no real access to the file system.