This phrase is all over the internet. They will say that something is free as in 'free beer' and free as in 'free speech'. I have never really understood this.
Are these the examples of two different types of 'free'?
This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information. See the FAQ for guidance on how to improve it.
Wikipedia on Gratis versus Libre:
Free beer means you do not have to pay for it. Free speech means you can say what you want. These are two different meanings.