You can relate a fingerprint stored on a device with a user and a password. To do this, you must import the LocalAuthentication.framework framework and use its methods. For more information look at the following link provided by the Apple documentation:
On the other hand, to link the fingerprint with a user and a password, I would use Keychain to store both in the secure site of the device. Apple provides us with a wrapper (you can include it with Cocoapods through this link: link ) to be able to implement the operations with this framework. Previously you will have to import the framework Security.framework in the options of the project.
Below is an example of how to use TouchID with Keychain.
Finally, answering your last question: No, it is not possible to detect between different traces stored in a device. The TouchID framework what it does is detect fingerprints and return success in case the fingerprint matches the ones stored and registered in your device or error, otherwise.
I hope I have helped you.