Government debt is money owed by any level of government; either federal government, municipal government or local government.
Sovereign debt is money owed by a nation to a bond holder.
Government debt can be held at all levels of government: city, county, state, federal. Sovereign debt is government debt but is guaranteed by the government; they will not default but will raise taxes to cover it.
The big difference between government debt and sovereign debt is that government debt is issued in the domestic currency, while sovereign debt is issued in a foreign currency.