Comparing a Spanish payslip with another country's
A Spanish payslip has two deductions: the employee's Social Security contributions, charged up to a monthly ceiling with a small solidarity contribution above it, and the income tax withholding, a single rate the employer applies to all of your pay. Most of the contribution bill falls on the employer instead, on top of gross, so a Spanish employee keeps a large share of gross while the employer's cost of the job is well above it.
Health care in Spain is provided by the national health system 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.