How much can there be to know about the standard screws used in computers? Well, that depends on how detailed you want to get. Wikipedia has an article on Computer case screws that might help explain some of the trends you’ve noticed about the screws if you’ve ever built a computer or messed around with the internal hardware enough.
The thumbscrew and the 6-32 screw have the same threading, so they could be used interchangeably though thumbscrews are typically used externally for securing the case side panels or other frequently accessed parts. The M3 screw and 6-32 screw might fit the same holes but the threading is off so using them in the wrong place will usually result in something getting stripped out. The self-tapping screw is usually used for chewing into plastic, most commonly case fans and securing them to a part of the case.
The article goes into much further detail about the 6-32 screw, the M3 screw, motherboard standoffs, and 4-40 jackscrews common with external connectors (like VGA). It can be a worthwhile read to have some more definite facts to the lessons you have learned from your hardware tinkering.
Computer case screws on Wikipedia.