difference between camera roll, photo stream and photo library

Camera Roll is temporary storage for all pics taken by or saved from the iphone itself. You should be importing these pics to your computer regularly as you would with any digital camera.

Photos stream is a cloud based service:

Photo Stream - Apple

Photo Library is where all pics synced from your computer to your iphone can be accessed.

I'll add:

Picasa should be able to see your iPhone as a camera when you connect the phone (though it may not automatically connect). All the photos in your Camera Roll (photos you took and images you saved in other applications) will be available to import into Picasa.

There has been discussion about trying to get Photo Stream working with Picasa, but I'm no expert. You could start here:

https://discussions.apple.com/thread/3688994?start=0&tstart=0

But, basically, Photo Stream is an Apple thing, and it isn't built to play well with Picasa.

I'm not sure what you're talking about when you say "Photo Library". Apple's iPhoto program has a photo library where all you photographs reside. From there, you can put them in albums, etc.

Photos go from my phone to the Photo Stream. How do they get to the Photo Library? What is the difference? Thanks.

See:

http://support.apple.com/kb/HT4486

and

http://support.apple.com/kb/PH2605

Both iPhoto and Aperture will automatically import Photo Stream photographs. You need to have your computer linked to the same iCloud account as your phone, you need to be running a recent version of either program, and your computer must be connected to the internet. The links above have more details.