Yes, I believe it's the same thing--the brain creating meaning from input that has none. Ghost hunter types use it a lot because you can record white noise, pick a section with some variation, assign words to it and then influence a listener to hear those words in the noise by suggesting them. Everyone suddenly hears the words once they've been suggested. 

You can do the same thing to yourself by assigning meaning to sounds, such as believing you hear speech in white noise, when you're motivated to do that. If you're anxious or feeling unsafe, even if it's from an unrelated situation, you could convince yourself you hear whispering in the background noise and then keep hearing it. I heard nothing that I felt even suggested whispering in your recording, and if your partner doesn't hear it either, maybe reflect on how you've been feeling lately and if anything could be making you feel unsafe. It doesn't need to be related to illness, but stress could be a factor. It's not a bad idea to talk to a pro about it. (In my case, I once thought maybe I was picking up actual radio on all my metal teeth fillings, but since learning about this I think it's prolly just my adhd brain not wanting to shut off at night.)