Cut-away locks are 'real' locks that have been cut-away to expose the pins and springs, allowing you to see what's happening when you insert the key or your lock picks. Clear locks are fully formed, but again, allow you to see what's happening. There is no quicker way to understand the process required to pick a lock than a clear or cut-away lock.
If you want to know how to pick a lock, this is a great place to start. A clear or cut-away lock and a set of lock picks and you're off. Practice locks are locks that have additional features to make learning the art of lock picking easier. If you want to learn how to pick a lock, a practice lock can help.