Forward is a direction (to the front); the opposite of rearward (towards the back). Onward is an exhortation: Keep going!

I agree with Glenn. Also, ONWARD is rarely used.

Forward > move ahead/ move in the direction of what is in front . Onward > from a place ahead/ where you are to what is further in front If you go forward , you will see the tree, but from then onward I don't know what you will see because I have not been so far before.