Sockrocker has it just right for the Christian music. It's a sort of folk/pop fusion. I call them 7/11 songs. Seven words repeated eleven times. There are a few Christian themed bands I enjoy, Mercy Me and some of Randy Travis' latest releases are examples. The bands I enjoy are bands that play Rock or Country with Christian themed lyrics, and not necessarily worship or praise music. The difference between worship and praise music, I have yet to grasp. I play in a worship band as a backup musician (will actually be getting stage time in a couple Sundays), but we tend to rock out a bit more than the mamby-pamby stuff I hear on the radio.
Being Indie has more to do with whether the band has a contract with a recording lable or not and has very little to do with style of music. There are gazillions of Indie bands. With the advent of relatively inexpensive studio equipment, including mixing and production equipment, it's now possible for a band to have their own studio and publish their own CD's. Then they can sell them through sites like CDBaby.com (great site, by the way) or their own web-sites. One of my current favorites along this line is The Duhks out of Canada. It's mostly music that doesn't fit neatly into Country, or Rock, or Folk. The Duhks play music that blends elements of Celtic/Cape Breton, Rock, Folk, and Bluegrass. Another of my favorites is Hillbilly Idol, a band whose slogan is "It's not your grandfather's country music, but he'd probably approve." This weekend, I'm going to be meeting up with a buddy on a fishing trip. He records music in his spare bedroom, publishes CDs on his home computer, and gives the music away as gifts to friends. He could be consider an "Indie." I call his style of music "campfire music", because that's where you're most likely to hear it. Good stuff.