Differences between "audio" and "sound"?

What is the difference between "audio" and "sound"?

Is it possible that a beeping noise could be considered one but not the other?

Audio is a more technical term, referring to sound coming from a recording, transmission or electronic device.

Sound is a more generic word and can be caused by any source.

So, if the beeping noise is coming from an electronic device, it could be considered audio, but usage is important. You would rarely refer to a specific, discrete noise as "audio". You could say:

They raise the audio for TV commercials.

But

I hear a beeping audio.

Sounds incorrect

I hear a beeping sound.

Would be better. Or:

I hear beeping in the audio transmission.

Or, depending on context, using audio as an adjective may be acceptable:

I hear audio beeping.

Audio is more generally considered to mean artificially generated sound specifically.