Use of g key in vim normal mode

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.

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.