No, that's not correct. S corporation shareholders are NOT subject to self-employment (SE) tax. SE tax is, of course, how self employed persons pay their FICA taxes (Social Security and Medicare taxes). But S corporation shareholders are not self-employed. To the extent they do work for the business, they are considered employees and subject to FICA taxes. So they are subject to FICA withholding on their earnings with the corporation paying its matching share of the FICA tax. They are not subject to SE tax in addition to the FICA taxes. Indeed, you are never subject to both FICA tax and SE on the same income.
Again, you are incorrect. Partners of a partnership are not employees of their partnerships. So there is no FICA withholding for their share of partnership profits. Instead, active partners (those that actually do work for the partnership) are subject to SE tax on their entire share of partnership profit.
So either way, Social Security and Medicare taxes are paid. With the S corporation, that's done with the FICA withholding on the wages of the corporate shareholder-employee. With a corporation, that's done by the SE tax that the partner pays on his/her share of the partnership profit.
Again, partners of a partnership do pay SE tax on their share of the partnership profit, and thus they pay Social Security and Medicare taxes. The tax rates are effectively the same for both. So you are going to have to pay that either way. The difference, however, is the base on which the tax is computed. For the S corporation shareholder who is an employee, the taxes are computed on his/her gross wages. For the partner of a partnership, it's his/her share of net profit of the partnership.
I'll give you an example that is simplified to illustrate the difference. Suppose that Joe and Steve are each a 50% shareholder of XYZ LLC that is taxed as a S corporation. They both are managing members of the corporation and do similar work for the corporation. The corporation would have had a net profit of $200,000 if it didn't have to pay Joe and Steve for the work they did, so each would have had $100,000 in net income from it. The reasonable compensation for the work they did (i.e. what they could have hired someone of similar skill to do the same work) is $85,000. So the corporation pays them each a salary of $85,000 for the year. The total FICA taxes for each them (the part withheld from their pay plus the corporate matching share) is 15.3% so Joe and Steve each pay $13,005 in FICA taxes. The corporation deducts the $85,000 in salary paid to each of them, so they now only have $15,000 in net income from the corporation on their return but they have $85,000 in salary, so in the end they both still end up with $100,000 of income on which they pay income tax.
Now assume that they instead operated as a partnership. Now they are not employees and do not get paid any salary. They each have $100,000 of net income from the partnership to include on their income tax return. They also must pay SE tax on that $100,000 of net income. So they pay 15.3% of $100,000 (actually just slightly less due to a quirk in computing the SE tax that I'm ignoring to illustrate the principle), so they end up paying $15,300 in SE tax.
So the bottom line here is that with both the S corporation and partnership they ended up with $100,000 of net income for income tax purposes. But what they pay in Social Security and Medicare tax is different. With the S corporation, they paid only $13,005 because the FICA tax is computed on the salary paid, not their entire profit. With the partnership they paid $15,300 of SE tax because that tax is computed on their entire net income from the partnership. Using the S corporation thus saved them each $2,295 in Social Security and Medicare tax because of that difference in what is used as the base for computing the tax.
Of course this is a very simplified example, and there are other things to consider when making the choice between S corporation and partnership than just the FICA/SE tax issue. Which is why you want to meet with a business attorney and tax attorney or other tax professional familiar with business taxation for advice on which is better to use for you right now. Bear in mind that it is pretty easy to convert from partnership to S corporation so you could start with a partnership and convert to S-corporation later on. That's what many small businesses do.