Coat typically refers to the length and the function of the garment. A jacket is shorter, but can still be long enough to cover your bottom.
Pants are not a requirement for jackets that cover your bottom!
Coat is usually an outer garment with sleeves made from wool, leather or heavy cloth material (e.g., fur) used as protection against rain or wind. Jackets are often worn in conjunction with trousers such as jeans, khakis or dress slacks. So you can wear a coat without pants because it’s functionally an overgarment whereas a jacket would need pants underneath so it wouldn’t drag on the ground when worn (unless it was really short).
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