> What is the distinction between government and state?

In a parliamentary democracy the "government" is the prime minister, president (whatever the titles are), cabinet ministers and the party that happens to be in power at any given time. The "Government" might be a coalition of 2, 3, or 4 medium sized political parties that have come to some sort of arrangement to have enough votes to pass a budget and laws. The "state" are the persons who perform the longer term functions of the state not directly controlled by the whims of any political thing that might happen in a specific year.

For instance when France made a decision to build its previous series of nuclear powered, missile carrying submarines, and the decision to build a new series that will enter service some time in the 2030s, that's implemented by the civil servants who run the state. Various political parties have waxed and waned and leadership has come and gone since the French nuclear program began, but various successor governments have continued it.

Less specific than that program, the state implements other basic services for the people of the country, all the things that have their day to day work done by people who aren't elected members of parliament. The parliamentarians who happen to be occupying various seats at any given time are the government.

In a more specific Canadian example: The government funding that comes to the CBC each year is actually from what would we would call the state. https://cbc.radio-canada.ca/en/impact-and-accountability/fin...

You'll see terms used like "the government has collapsed as the result of a non confidence vote" or "there's been a leadership challenge inside the government (eg: how Trudeau lost power recently)", it doesn't mean the functions of the state have collapsed.