"The phantasms are unlike any spirits I have ever seen on Sanctuary. They bear a resemblance to lesser demons, but the souls of demons are always reborn in the Hells... I suspect the phantasms may be the remnants of some early nephalem, those born more demon than angel."— Archangel Tyrael(src)
Phantasms are a form of spirit, but different from those usually found in Sanctuary. Tyrael theorized that they may be the remnants of early nephalem who manifested more demon than angel. It is known that an Umbaru priest who returned from a visit to the Unformed Land returned as a Phantasm.
Phantasms are absolutely identical to Wraiths, except for they move a bit faster an generally do not attempt to attack in melee. They are phasing through the walls and leech life from afar just like Shadows and Wraiths. They are only encountered in Act V, and only in tunnels below the Westmarch and in the nephalem ruins. Those in tunnels are bright orange in color, while the ruin-dwelling Phantasms are blue.
Visually, they are transparent demonic figures, as opposed to human-like Wraiths.