As others have said Sean-Nós is a term which is usually reserved for singing in Irish. The term tends to be much abused and is used by some people to define any unaccompanied singing. All unaccompanied singing is not sean-nós, nor is a song sung in Irish necessarily Sean Nós. I'd find it hard to say exactly what defines this particular style, but I know it when I hear it. That is not to say that other styles of singing are any less traditional, or good than Sean Nós, in fact I find I really like to hear this particular style in fairly small doses, but that's my own preference.

Sean Nós shares much of its ornamentation with other Irish singing styles and many who sing in English will have a style that is influenced to some degree or other by it. As I usually say in topics of this nature I'm much more interested in hearing people puting the style into practice than in long debates about whether it fits into a particular category.