LLC is a type of legal entity (like a Corporation) while S-Corp is a tax classification (like C-Corp, partnership, etc). You can elect to have an LLC taxed as an S-Corp, C-Corp, partnership, and so on. Legal entity choice such as LLC vs Corporation impacts the administrative requirements (filings, meetings, etc) and ownership/management structure (Corporations have shareholders, directors, officers but LLCs have members and can optionally appoint officers). Tax classification impacts whether or not tax obligations are passed through to owners as in partnership or sole proprietor taxation vs tax obligations belonging to the legal entity itself with additional tax obligations for owners as in C-Corp and S-Corp taxation. See the link for a more detailed explanation of considerations when organizing a legal entity and choosing a tax classification.
There are a variety of reasons that some large businesses are organized as LLCs. One of the most common reasons is simply to set up a subsidiary entity that is simple to administer and disregarded for tax purposes (because the tax obligations are passed through to the owner entity) - this is the case for Chrysler, now FCA US LLC, which is the US subsidiary of Fiat Chrysler Automobiles, NV .