Both are means of organiizing and manipulating information.
The spreadsheet has more mathematical talents, and is primarily for use in calculating.
The database has a larger variety on ways to organize and display the information, and can do many of the calculations performed by the spreadsheet.
You can get a good idea of the differences between the two by looking at the templates that came with your AppleWorks application. You'll find them in Starting Points.
Which you use would depend on what you want to accomplish. If you have a specific task in mind, and can't decide which to use, post here with a fairly detailed description of the task you want AppleWorks to do.
Regards,
Barry