Envision a large box and inside that box are one or more (as many as 20) smaller boxes. A "System" is that large box. A "Group" would be one of those smaller boxes.
Your example has "S0" which is actually the letter "S" for system and zero "0" which is the quick key for that system. GRP indicates the quick key(s) for the group(s). While it seems strange, even though you can have 20 groups, you can have only 10 group quick keys.
Systems can have System Quick Keys from 0 to 99. Groups can have Group Quick Keys 0 to 9.
System Quick Keys 0-9 are "one button press" operation. Thus for example a system with a System Quick Key of 5, requires only pressing 5 on the keypad to toggle on/off. If you assign a System Quicky of 10 or higher, then you press the period button first, then the two digits. In other words, a System Quick Key of 15 requires ".15" to toggle on/off.
There are two sides to the argument: SQKs 0-9 are that one button press. But you can inadvertently bump a button and toggle the SQK. With SQK 10 and higher, you have to press the period button first, lessening the chance of inadvertently toggling the SQK.
Toggling Group Quick Keys is a little more "dicey". Your scanner has to be actively scanning the system before you can toggle a Group Quick Key associated with that system. To do so, you would press the Function button, then the associated Group Quick Key number.
As does the previous poster, I typically assign channels (either talkgroups or conventional frequencies) based on the service (police, fire, EMS, etc.)