Is the Swiss C permit the same as citizenship, and does it help me naturalise?

The Settlement Permit C is permanent residence, not Swiss nationality. It is, however, a building block toward citizenship. Ordinary naturalisation is open to foreign nationals who have lived at least 10 years in Switzerland (with 3 of the last 5 years before applying), hold a C permit, and meet integration and language requirements. So the C permit does not grant a passport or voting rights, but it is the residence status you must hold before you can apply for ordinary naturalisation.