About the Expressions "Stick Around" and "Stay Tuned"
What comes to your mind when you hear a TV/radio broadcaster says the phrase "stick around" or "stay tuned" at the end of that TV/radio show? I'd like to know how native speakers feel about it and how those expressions are used, as well as the difference between both.

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Answer

In this context they both mean 'keep listening to this radio show' but 'stay tuned' only works in the context of listening to the radio - you 'tune' in to a radio station.

'Stick around' - is a more informal way to say 'stay here'.  So you could use it in other contexts too.
Example:  We went to the party but we didn't stick around long because it was quite boring.