Use of g key in vim normal mode
Solution 1:
There's no greater connection to g-commands: it's a mixed bunch. It is an easy prefix and the unbound keys were getting extinct so the less-used maps found a good place behind g.
Solution 2:
Simply you're talking about two different things. In some cases g is the short way of "global" (for range command for example), for line moving the g stands for goto.
In VIM commands are often shortened for quick of use.
:help global may help
Btw: for line navigation I've always used the :<lineno> syntax.