One is an electoral district approximating to the English constituency, but typically the size of a province or region, depending on the election.
The other is a subdivision of city comuni, roughly equivalent to the municipal arrondissements of Paris or the London boroughs.
For elections to the European Parliament, Italy is split into 5 circoscrizioni, typically of 4–5 regions joined.
District councils started to appear in the 1960s, but municipal circoscrizioni were formally recognised in law in 1976, and their powers extended in 1990.
Each circoscrizione now need to have at least 30,000 residents, and typically corresponds to historic divisions of a city, but could contain multiple frazioni, località or quartieri.