Comparing signals recorded using diffrent methods Suppose we have two signals( focus to audio) recorded with different methods,
or more simply, suppose we have two audio signals recorded with different microphone, and  we want to confirm that these signals are of the same audio.

What are the available alogorithms or libraries that make this possible?
Different flavors of cross correlation are probably the best choice here. It really depends on how exactly the recordings are different. Two microphones side by side behave very differently than two microphones in different spots in the room. Your best method will depend on a clear understanding of what your application needs to cover and what doesn't.