It is legal and in some areas common to stand and be elected to two different parishes. (I have stood for two - three miles rule for one - I live yards from the parish boundary, and the work rule for the second). In rural areas the reason being is to help working together and the bridge between the villages/parishes.
The restrictions are you cannot stand in two wards/divisions or constituencies for the same parish (e.g. East and West wards), district or county council ward or Westminster.
Each council is a separate legal entity so being elected to both is fine.
In the most extreme example it is legal to stand for the Scottish Parliament (living in Scotland) and the Welsh Senedd as Wales does not have a residency rule.