Forward you can use to talk about some future event, like "I am looking forward to seeing you". You also use it for all things, that have to do with time ("I have to move forward in my life." "Fast forward" etc.); whereas you use ahead for direction or continuation - literally and figuratively both ("Go ahead"- meaning: continue what you are doing or I will catch up with you later, but you can go now/ right away "he is way ahead of his class" meaning he has some kind of advantage or is better than his classmates)
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