The reason for the 4 wire is because since about 1992 the NEC (National Electrical Code) has required separate ground and neutral wires whenever the box is considered as being a subpanel. For your purposes, the generator is considered to be the main panel and your house is the subpanel.
At the main panel you only need two hot wires and a neutral, which is also connected to an earth ground within about 10' of the panel, but at the subpanel you are supposed to have 4 wires. The subpanel is supposed to be wired with all the bare ground wires to one bus bar that also is grounded to the metal of the box, and then grounded back to the main panel via its own wire. Then all the 110V white neutrals are landed on another bus bar that is NOT grounded to the metal of the subpanel box. Instead, it is wired all the way back to the main panel where it is connected to the same ground bar that the other ground wire is connected to, and then to the earth ground.
As I recall, it has to do with the fact that if a ground rod is driven at the main panel and another ground rod is driven at the subpanel, they will almost never be at the same potential due to differences in ground moisture, etc. By wiring the ground back to the main panel a ground rod isn't needed at the subpanel, but can be used if wanted (it doesn't really do anything, so why bother). The problem with having two ground points at two different locations w/o having a ground wire tieing the two together is that they won't be at the same potential, and electricity can do some very strange things if something gets shorted.
It will work just fine the way you have it, but I wouldn't put another ground rod at the generator. With only 25' of wire I wouldn't even worry about it, and there is no good reason to tie the two grounds together at the generator. Just use it like before and consider your house as still being the main panel instead of the subpanel.