Cat back is a whole exhaust system from the cat converter, back to the muffler... An axle back is simply just the muffler itself usually... The cat is usually what restricts your perfromance when it comes to exhaust... So a new hi flow cat will generally mean increased performance and a different tone from the muffler, a new muffler could mean increased performance, and a different tone... And mendrel bent piping, which comes with cat backs usually, also helps...

Cat back:
http://www.cyberauto.com/images/crx-cat-back.jpg

Axle back:
http://www.stlsupra.com/honda/exhaust/axleback.jpg

But if u want to go the cheap route, and live in an area that dosnt have emissions laws, I say get a nice muffler, and a hi flow cat and call it a day...