Are the songs just familiar from the movie? I saw part of it once as a kid but I don't even remember anything about the movie.
They only cut two songs from the movie: "Lovey-Dovey Baby" and "High Times, Hard Times" (that won the Razzie Award in 1992 for Worst Song). Both were the songs that Ann Margaret sang. The character is still in the show, but she just has one (much better) song called "That's Rich".
There are actually quite a few new songs: Pulitzer has a song in Act 1called "The Bottom Line" that is reprised in Act 2, but it's not much.
Katherine, the female reporter that replaced Bill Pullman's character from the movie has an awesome new song called "Watch What Happens", which is also reprised in Act 2. She's also the new love interest for Jack, so they have a duet called "Something to Believe In". Jack also sings "I Never Planned on Someone Like You" in Act 1 when he's trying to flirt with her.
The Brooklyn gang also has a brand-new song, called "Brooklyn's Here."
The rest of the songs are from the movie, but they've been majorly re-written. "Santa Fe", Jack's big song, is an entirely different song now. It now opens the show (he's sings it to Crutchie), and it closes Act 1. He's no longer a wannabe cowboy like he was in the movie, he's now a talented artist. He paints the backgrounds at Medda's theater and they use his drawings to help settle the strike.
They also took what seemed like a throwaway song from the movie, called "Once and For All" and made into almost an anthem for the strike at the end.
It's very faithful to the movie, but they've also re-worked a lot of it for the stage, and got rid of stuff that didn't work in the movie (I love it, but I remember how badly it tanked when it first came out).
The show is awesome. I've seen it twice now, and it was even better the second time.