I see no intrinsic difference between overcoat and long coat. Both extend to wearer's knees. The term overcoat seems to be more commonly-used. Even Wikipedia redirects "Long coat" to "Overcoat".
Coats are also technically supposed to be worn over jackets as well. For those who downvoted, I would like to know better proposed alternatives or why would you think long_coat and overcoat should stay despite they seem interchangable?
from reading the wikis my impression is that a long coat is only long while an overcoat is also heavy, so a lab coat can be a long coat but not a heavy coat
It looks like long coat was created to be the coat version of long dress or long skirt, while overcoat was created to be similar to overskirt. The example image given for overcoat is just coat on shoulders and it looks like the very specific requirement is for a jacket whereas long coat is agnostic to this. This is what I get from reading the wikis and looking at some of the tagged posts.
We have plenty of posts where a coat isn't worn over a jacket and I'm not talking about labcoats which have their own tag, they're more like fashionable or thin coats. I'm not particularly sure what you were aiming for there by saying that "coats are technically supposed to be worn over jackets" but it's probably not too relevant to the specific concepts these two tags are trying to tackle (length and style, not the isolated article of clothing itself which is agnostic to a jacket's presence).