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Is there a difference between when I should use "אוטו" vs "רכב"?

I speak Hebrew as a second language, and probably worse than most people expect - I live in Israel, but my Hebrew is still not that great. 

I ride with a cycling team, and one thing that we do is to shout if there's a car on the road, to alert the other riders to be careful. I have at times shouted אוטו and then been told I should have used רכב instead.

Is there a functional difference between these two words? I'm aware that רכב is an ancient Hebrew word that meant "chariot", and that אוטו comes from the English "automobile", but as far as I know they both meant the same thing. Is it that one is more formal (e.g. "car" vs "automobile"), or do they have slightly different nuances, or what?