Sure looks like a coal stove. We still have an old upright from the fifties that was enameled so it would look a little nicer if in a formal room in the house. I'll have to go look see if the shaker grates actually shake/move or if the ash just had to fall thru them. We burned wood in it. Vertical.
It looks like a warm morning 523 but I don't think it is a Warm Morning as I don't remember a name on it. I don't think any coal was ever burned in it.
Are there rocker grates in the bottom? Any firebrick or just cast iron. Looks like a coal burner to me.