AutoCorrect and QuickCorrect are the expanders that come with Word and WordPerfect. They use a simple two column format (short form and long form) and appear to have been designed mainly to automatically correct spelling mistakes and to insert blocks of texts.
There are about 30 others. These expanders go far beyond the capabilities of AutoCorrect and QuickCorrect. Some offer visual advisories so you can see a list of short forms before you type them (e.g. Instant Text, Shorthand) or give you a reminder after you type one (FlashForward, Speedtype, QuickScript). Some allow you to import your short forms from other expanders (Instant Text, Shorthand). Expanders offer numerous other features such as line counting, statistics, formatting options, incorporation of macros, importing files from other expanders, etc.
If you do a lot of typing, using a typing expander is well worth it!
A typing abbreviation system is designed to help you remember your typing abbreviations and make them easy to access as you type. Without using a system it can be difficult to remember the hundreds or thousands of abbreviations you may have.
One commercially system available is my (Jon Knowles) ABCZ Typing Abbreviation System for Instant Text and Shorthand/Speedtype. Mary Morken's Add-on Abbreviations is another such system and is importable into certain expanders.
ABCZ Typing Abbreviation System (Guidelines to building your own abbreviation file)
(Basic information on a dozen or more expanders)
MT Daily, Speed Typing (further information on expanders and several typing abbreviation systems)