The idea of uniqueness, specialness, and the tautological descriptions of a chosen people with an important mission, destiny or messianic role to play in the world is not something that is confined to the Russians. It's a feature of nationalisms elsewhere.
Eurasianism can be distinct from nationalism but does draw from intellectual currents (anti-western, or in response to western Europe but like the classical Eurasianists doing so by borrowing from western thought/intellectual heritage) that have fed into previous manifestations of Russian nationalism, not always seen as useful to the Russian state. I don't think Putin is a Eurasianist. It's that abuse or misunderstanding of the term again. Nationalists with reassertion on their minds and in their policies while being aware of Russia's geographical reality is not the same thing. The nationalists are wanting to deal with the reality of US-led containment/encirclement, and imperialist competition for control of the former Soviet Union's periphery.
Correct me if I'm wrong but Dugin's vision of the world does not involve nationalism or even nation-states. It's more radical than that. The world would be divided and ordered into civilisational zones or areas containing a mosaic of ethnically different peoples who nevertheless share historical and cultural bonds, all living within a strict hierarchy but supposedly harmonious because of those spacial/cultural links. The Russians and their superior culture, however, would (to paraphrase Laruelle earlier) be the cement in one particular area that holds everything together and the rest of the peoples within it merely the bricks of Russian dominance. It's still an imperialistic ideology. The Russians are destined to rule one area. An undemocratic, caste-like (but technologically advanced) conglomeration of peoples. A mixing or miscegenation of peoples (except for the elites) from other civilisational areas jeopardises the order. He has drawn from European 'new right' thinking and Traditionalism in this vision.
How would I draw a distinction between nationalism and Eurasinism? We'd need to look at a particular Eurasianist current, although I've crudely outlined Dugin's world.