Richard Spencer, a prominent leader of the 'Alt-Right' is often referred as a white supremacist by the western media. In December, 2016 CNN published an article which referred to him as a 'white supremacist'. His Wikipedia entry also identifies him as a white supremacist.
Richard Bertrand Spencer (born May 11, 1978) is an American white supremacist. He is president of the National Policy Institute, a white nationalist think tank, as well as Washington Summit Publishers. Spencer has stated that he rejects the label of white supremacist, and prefers to describe himself as an identitarian. He has advocated for a white homeland for a "dispossessed white race" and called for "peaceful ethnic cleansing" to halt the "deconstruction" of European culture.
The first two lines of his wiki entry are contradictory. In the first line, he is referred as a white supremacist and in the second, his think tank is flagged as 'white nationalist'. If he is promoting white nationalist thought, then he is a white nationalist not a white supremacist.
You might ask, what is the difference between a white nationalist and a white supremacist? The answer to this question is:
What’s the difference between white nationalism and white supremacy?
.. “White supremacy is based on notions of racial superiority that date back to the middle of the 19th century, the notion that the white race is superior and deserves to dominate other groups.”
White nationalism is different, but still related to this idea.
“White nationalism, as opposed to generic racism, is an ideology that calls for the creation of a homogenous white nation,” Hawley, who recently wrote a book on the subject, said. “Within that movement, people disagree on how this can be brought about, but they agree on that long-term goal. In this sense, white nationalists are far more extreme than ordinary conservatives when it comes to issues of race.”
Reference: USA Today
He identifies himself as an Identitarian. The term "Identitarian" is a new invention by white nationalists to make white nationalism attractive to the general public.
According to Christoph Gurk one of the goals of the Identitarians is to make racism modern and fashionable and they have close connections to Hungarian and Polish Neo-Nazis, according to Anna Thalhammer. There has also been Identitarian collaboration with the white nationalist activist Tomislav Sunić.
"Identitarians" aren't white supremacist but they sure collaborate with Nazis and white supremacists. So, it is inaccurate to call Spencer a white supremacist.