Generally, an S-Corp is a pass-through entity where taxes are deferred until the money "passes through" the business to a taxable entity... such as you personally. Now if your S-Corp has employees, then the S-Corp would be paying the employer side of the wages paid to employees. With an S-Corp, it is perfectly possible for an owner or shareholder (such as yourself) to also be a W-2 employee.
As for distributions reported on a K-1, I think the S-corp pays the corporate side of taxes (medicare and SS) and the recipient of the K-1 pays their side. It's perfectly possible for the S-Corp to pay the K-1 recipient's taxes "on behalf of" said recipient. But I don't see any place on the 1120-S K-1 for any taxes paid on the recipient's behalf. .
