Custom applications on Android are served as APK files, usually app from the app store have excessive permissions, these permissions are used to sell your data to advertisers and are not usually needed to run the actual program, a custom rom program is usually made by people with an open source mindset which will ask only for the necessary permissions to run the program.

Be careful when installing custom roms/apk files, make sure the source is trusted, the open source nature of the software means there is a possibility of malicious actors creating programs to manipulate/steal data, always check and then triple check the validity of the group that created the program and the source.
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