Suppose amount of money an employer is willing to pay for an employee is $100,000. For the employer, if there is a $20,000 payroll tax, then the employer would only pay the employee $80,000 to keep the total cost at $100,000. If the employee pays the tax, then the employer will pay the employee $100,000, then the employee pays $20,000 and has $80,000 after taxes. Either way the employer pays $100,000 and the employee gets $80,000. It doesn't matter which party is paying the government $20,000*.

Now, there are other tax schemes that aren't based on how much an employee is paid, but that is a completely different matter.

And FWIW sales/vat tax is somewhat similar. It doesn't matter if the buyer or the seller pays the tax, either has the same effect on the total amount paid.