Hindi Music Question: Shani = God or Saturday?

Hello there, in the last year or so we've gotten a Hindi radio station (Radio Salaam Namaste) in our area that I listen to on occasion. Sometimes the music is really fascinating despite the fact I don't understand a word of it. However, I did notice that in many songs, I keep hearing "Shani" repeated in the main chorus. Well, I finally got around to looking it up on Wikipedia, and found out that Shani is the God of Saturn for Hinduism (makes sense), but Shani-war is the Hindi word for Saturday. Considering the deep religious and cultural affiliation apparent in many of the traditional songs played on Salaam Namaste, I figure it could go either way.

So I was hoping some of our Hindi-speaking people could perhaps clarify for me the significance of "Shani" in Hindi music.

Is it usually just a reference to Saturday? Or the avoidance of bad influence? Or lessons learned? Or a play on words? Or am I completely mishearing the word altogether and it's actually a reference to some Bollywood actress or something named Chani or something?