Yeah, it's a bit circular to say that a commoner isn't common because it's become an insult to call someone common.
My head's going around in circles now!
In law, the word "commoner" simply means "someone who is neither the Sovereign nor a peer." That includes any member of the Royal Family who is not a peer, such as Prince William and Princess Anne. It also includes any member of a peer's family, including someone who holds only a courtesy title, such as the Earl of Arundel and Surrey (eldest son of the Duke of Norfolk) or Lady Victoria Hervey (a daughter of the 6th Marquess of Bristol). That is to say, the vast majority of UK citizens. It has never meant anything else, with a few exceptions for example:
In some British universities (notably Oxford and Cambridge), a commoner is an undergraduate student who does not hold either a scholarship or an exhibition.
Some people have rights such as fishing, grazing cattle etc on areas of land such as ancient estates, forests, commons and so on, and these people are called commoners. A commoner of such-and-such a piece of land would have the right to graze his sheep on that land even though he is not the owner.
None of the above uses of the word "commoner" have ever carried any insulting implication of vulgarity or lack of breeding or culture or manners.
HOWEVER,
For several hundred years, the word "common" has been used as an insult or slight by people who wish to convey that the person being referred to is less socially polished than the speaker. It comes from the ordinary English adjective "common" which means ordinary, widespread, ubiquitous, run-of-the-mill etc.
Any confusion between the two words is a mistake.