The difference between the two is subtle, and it a complicated mix of corporate law and taxes.
First, let's talk about a company without going into taxes at all. A company is something that exists under state law. People like to refer to it as corporate personhood. State laws provide the basis for creating companies. There are different types of companies, and all states let you create a company that is a corporation or an LLC.
A corporation is your traditional company with shareholders and stock. Very small businesses typically don't get created as a corporation because there is a lot of formalities and paperwork under state law that just isn't worth it.
An LLC is a more recent type of company that has owners but doesn't have stock. It is easy to create an LLC and, in many states, you just have to file a simple annual report. Most very small business do this because it is so easy.
Notice that I haven't yet mentioned an S-Corp. An S-Corp is not a type of company but a way of taxing a company.
Second, let's talk about taxation. After you have created your company (an LLC or a corporation), you have options about how you would like to be taxed by the IRS.
For an LLC, you have two options. You can have pass-through taxation (since you will be the sole owner) or be taxed as an S-Corp.
For a corporation, you also have two options. You can be taxed as a C-Corp or be taxed as an S-Corp.
I won't go into the details of pass through, C-Corp, and S-Corp taxation because this is already a long answer.
Two Types of S-Corps
From the above, there are two ways of creating a company taxed as an S-Corp:
- Create an LLC under state law and elect S-Corp taxation with the IRS
- Create a Corporation under state law and elect S-Corp taxation with the IRS (I assume this is what you mean by an S-Corp in your question)
So what are the differences between the two?
If you go the first route, you get the benefits of S-Corp taxation, but you have lower burdens under state law of maintaining your company (e.g., you don't need shareholder meetings and stuff like that). An LLC taxed as an S-Corp is a popular option for this reason.
If you go the second route, you have the same taxation, but you have to deal with the burdens of maintaining a corporation under state law.
Some people say that a Corporation gives you better protection than an LLC with regards to protecting your personal assets in the event that your company gets sued (an argument for the second route), but I suspect that isn't the case and I've never seen a cogent justification for this.