Is it true the the categories of application software are mutually exclusive?

No. Lots of applications are capable of doing some of the things that others can do. There are things a spreadsheet is mainly used for that it is also possible to do in a database or even in a Word processor, like calculations. You use the software that is best suited to your task. You can do calculations using a Word processor, but a spreadsheet is better for that. You can filter data using a spreadsheet, but a database is better for that. Because software is not mutually exclusive you can get the to work together and do different things with the same data or transfer work from one to another.