Both "move on" and "keep going" have the meaning of "moving forward". However, the biggest difference between them is
"move on" will NOT stay with the same "person" or "thing" that one has been dealing with, but just move forward without it.
"keep going" will stay with the same "person" or "thing" that one has been dealing with, and move forward with it.
2011-12-31 02:28:12 補充：
After searching the entire field without any result, police has finally moved on.
When he arrived, all his friends have moved on without waiting for him.
They stayed for a few days before moving on.
Let move on to the next question.
2011-12-31 02:30:33 補充：
The public opinion has moved on a great deal since then.
It has been a nightmare, but I just want to forget about it and move on.
We moved on as requested.
2011-12-31 02:33:47 補充：
They forced themselves to keep going even though they felt exhausted.
The truck kept going and disappeared from view.
The money will keep us going for another year.
Our sponsor kept our art studio going for as long as he could.
2011-12-31 02:37:24 補充：
If you are going through hell, keep going.
Just keep going, you got nothing to lose.
OK, I hope that is enough to see the difference!