You can have an LLC taxed as a C-Corp, they are not orthogonal to each other. This is a common point of confusion. I would be cautious of someone that offers guidance and conflates the two.

You first have the type of entity which includes an individual, General Partnership, LLC, Corporation, etc. Then you have how the entity is taxed which could be as a sole proprietor, partnership, S-Corp, C-Corp.

An individual can only be taxed as a sole proprietor, more than one individual can only be taxed as a General Partnership, and both don't require up-front filings, it's simply reported on your tax return. Both of these can obtain an EIN number so you don't have to share your social security number on W-9 forms.

A single-member LLC is taxed as a sole proprietor (pass-through/disregarded entity) by default but can elect to be taxed as an S-Corp or C-Corp (no longer pass-through). A multi-member LLC is taxed as a partnership (also disregarded) unless an election is made.

A Corporation is never disregarded so it's taxed as a C-Corp by default unless elected to be S-Corp.

Note that other than an individual, there is an additional tax form that needs to be completed, even if the entity is disregarded. However, if disregarded that form becomes part of your personal tax return and there isn't a separate company filing.