The basic definition can be found here: IRS Definition
One thing that is great about churches is that they don't have to file a 1023 (application for exemption) or a 990 (annual report). (This is a little different if you have payroll.) IRS regulationjs define religios worship as: "What constitutes conduct of religious worship or the ministration of sacerdotal functions depends on the interests and practices of a particular religious body constituting a church." Basically you set the rules and practice them.
I also have a great book, (2005 data) Church and Nonprofit Financial Guide
Reads like a tax book, no matter what they say about easy to understand. You pretty much have to have a financial mind set for any of this junk. You can probably find it at your library as well as many other books for starting a nonprofit. There are advantages and disadvantages of both. I'm more than happy to lend a hand here. I'm not an expert, but I know a few things.
We went nonprofit instead of a church because it gave us the ability to present in schools even though we 'preach' the Code of Chivalry. Ah, I'm ahead of myself. We teach about historical combat and knighthood in the middle ages and the society of the time. Chivalry was a very important part of society and the knight. We could have gone the route of being a church of chivalry, but decided against it.
I'd have to dig a little deeper and re-read some things to make sure I'm giving the best answers to you. It's been a while since I've researched it and have concentrated so much on the nonprofit stuff lately that the church stuff is a little buried.
I'll PM you with my email and contact info, or we can continue to discuss things here.