Comparing an Italian payslip with another country's
An Italian payslip takes the employee's social security contributions, mostly for the state pension, then income tax on what remains after the employment tax credit, then a regional and a municipal surtax on the same income. At low incomes it also adds two payments the state makes through the employer. The employer pays a much larger share of the contributions on top of gross, so the employer's cost of the job is well above the salary.
Health care in Italy is provided by the national health service and paid for from general taxation, so it is neither a deduction on the payslip nor a purchase in the household budget. Against an American state that matters most, because the American net figure has not yet paid for health insurance. Against another European country the comparison is closer, but the same risks are split between tax, contributions and private spending in different proportions on each side.
Equal purchasing power, not the exchange rate
The second gross salary on this page is the one that buys the same basket in the other place, derived from official purchasing power parities. Both sides then go through their own payroll rules, and what is left is brought back to one set of prices in the row labelled real take-home. Because both columns begin with the same real income, the difference at the end is the tax and contribution systems and nothing else.
Where the other side is a US state, its price level is chained rather than measured: Eurostat publishes a parity for the United States as a whole, the Bureau of Economic Analysis publishes an index placing each state against the American average, and the state figure is the first scaled by the second. The page notes this above the tables. Against another euro country the exchange rate is one to one, so the whole difference in the second salary is prices.