Typically what separates a canyon from any ordinary stream is the narrow passage created by erosion into bedrock, creating beautiful sculptured walls and spectacular waterfalls.
Canyoning can be treacherous. There are risks associated with scrambling down uneven, slippery surfaces and abseiling in wet, cold conditions. Several fatalities have occurred in this sport as a result of flash flooding. the most infamous of which happened when a group of tourists on a commercial canyoning adventure trip were drowned in Switzerland in 1999. 
Several sites contain information about canyons near Sydney:
Site about Utah area: