I was on a train that was headed/heading (for) home. I was on a train headed/heading (for) home. The above are all similar but I agree with the idea that using ‘heading’ gives the sentence a different feel. It puts you in the action a little more. I wouldn’t go so far as to say it sounds incomplete, but I would be inclined to use ‘headed’ if the statement was going to stand by itself. Note that if the destination is ‘home’, you can omit the ‘for’ but for other destinations it’s required. Q. Where were you at midnight? A. On a train headed for Chicago. I was on a train heading for home when the passenger sitting across from me started telling me his life story. Etc.

Every verb has two adjective forms: the present participle and the past participle. Let's use "play" as an example. The participles are played and playing. The present participle turns the action of the verb into a timeless abstraction. So, "playing" contains the idea of the verb "to play" abstracted as an adjective that has neither past, nor present, nor future. The past participle turns the action of the verb into a timeless ACCOMPLISHMENT. The accomplishment may be past, present, or future. Here are some examples. Notice how the participle "played" gives no information about time frame: The game is played like this ... Poker is the game played yesterday. Tomorrow, the masterpiece played at Symphony Hall will be Beethoven's Fifth Symphony. So, let's return to your example. The participles are "heading" and "headed". They differ in that "headed" speaks of something done or decided, whereas "heading" does not. "The train heading home" conveys the notion of a train moving towards home. It does that and nothing more. "The train headed home" does the same together with the accomplishment of being set towards home. It is possible to imagine one being true without the other. For example, suppose you board a train that you thought was headed for Seoul. Imagine that a few minutes later you realize you have taken the wrong train. You would say to yourself "Oh my gosh! This train is heading home! I'M HEADING HOME BUT I AM NOT HEADED HOME. I was headed for Seoul and I still am headed for Seoul. I must change trains at the next stop."

To me they are the same. You can add “that was” but it’s not necessary. It is really only a complete sentence if it is the answer to a question. Where were you when I called you? We were on a train headed/heading home. Full sentence We were on a train headed home when you called us.

Hello

Both sentences are correct and I think this is a stylistic difference. They mean the same thing, it's just a different way of saying the same thing.