Actually, both options are not correct. You would want to say "I ride the train to work every day" or "I take the train to work every day." Remember to add the article "the" :). "I ride on the train" isn't incorrect, but it sounds awkward, so I would recommend not using "on." However, you can say "I am on the train" or "he's on the train" and that would be fine.

Children say," I like to go for a ride on the train" but adults say, "I go on the train/ take the train to work"

I agree, just the use of the word "ride" sounds strange: I think you are on top of the train, riding it like a horse. Use "I take the train" or "I go by train".