A sparse disk image is an automatically expanding disk image. In other words, you can create a 50 gigabyte sparse disk image, yet only put 5 megs inside it. The disk image will only take up five megs of space on your harddisk, but will be capable of storing up to 50 gigs of data should you choose to add it. Note that it auto-expands but does not auto-contract. In other words, if you delete files from the image, you will not regain any free space on your harddisk (although you will on the image). Disk Utility can be used to "shrink" a sparse image, reclaiming any unused space on the image.

A sparse bundle is essentially the same thing, the only difference is that while a sparse image is one giant file on your disk, a sparse bundle is actually lots of small files (8 megabytes each). They work and look the same way, but you can right-click on a sparse bundle, select "show package contents" and see the individual 8 meg "bands".

The sparse bundle was introduced with OS 10.5 in order better support Time Machine (Especially with FileVault, where the entire home directory is a sparse bundle). Previously, a backup programme would see the image as one file, and if any changes had to been made to it, it would have to recopy the entire image. With sparse bundle, it can only copy the bands that have been changed since the last backup, so the backups are much quicker. It also is likely to decrease the chance of data loss, as you could conceivably restore parts of a damaged image.

Basically, if you want a sparse image, use the sparse bundle under 10.5. Only use the sparse image if you need backwards-compatibility with earlier versions of the Mac OS.

It looks like I may have erred in regards to claiming that you could shrink a sparseimage/bundle with Disk Utility. That said, it's still really easy to do. Just fire up Terminal and enter the following

hdiutil compact /path_to/yourimage.sparseimage

Or just hdiutil compact, then add a space and drag the image into the Terminal window to complete the path.

There should not be, and I myself have never experienced one (I use FileVault so have had lots of experience running the entire OS using both sparseimages and sparsebundles). In fact, if anything, breaking it into bands should increase reliability (if a single bands is corrupted, you may still be able to access your other data or even restore the damaged band from a backup), and in theory not having to write all data to one enormous file could yield performance increases when working with large images (I have not noticed a difference one way or another).