Nope,that’s not correct. Even in English health insurance is not tax, unemployment insurance is not tax...
And by the way what you call ‘charges’ is historically‘cotisations’ (fees).
In my circle of acquaintances, the distinction lies not in what the money is funding (e.g. health care), but in where it's going:
Health coverage goes to some entity that isn't the government and is usually optional, so it's viewed as a benefit and taken into account when computing total compensation.
Unemployment insurance on the other hand is taken out of every paycheck and handed to the government without an opt-out. Yes, of course you get something for it; the whole point of taxes is that society gets something in return. They're still taxes.
Health coverage goes to some entity that isn't the government and is usually optional, so it's viewed as a benefit and taken into account when computing total compensation.
Unemployment insurance on the other hand is taken out of every paycheck and handed to the government without an opt-out. Yes, of course you get something for it; the whole point of taxes is that society gets something in return. They're still taxes.