I understand 着 as something static, like 门开着 - the door is open. It is not currently being opened (like 正在 would indicate), it is open and just continues this state of being open. But I don't really understand the difference for something like 下着雨 and 正在下雨, wouldn't they both mean it is raining?
basically correct. '正在下雨' can occur in specific situations. like： if it's raining outside and a child wants to go out and play football,then mother gonna say: '外面正下着雨呢，不许去，淋浴会生病。
