This is one of those difficult questions to answer because the issue of identity is often highly plastic for borderland area like Galicia where national identity does not fit into easy categories. It's always dangerous in studies of nationalism to assume that ethnic/national identity is innate or primordial and to assume nationalist activists reflected a majority opinion. For this answer, I'm also going straight into the nineteenth and twentieth centuries.

Generally speaking, Ruthenian refers to an ethno-linguistic group that resided in the Carpathian regions of Galicia. The predominant Ruthenian religion was Greek Catholic and were under the political authority of the Hapsburg empire after the first partition of Poland in 1772. The Austrian state gingerly encouraged a Ruthenian identity to discourage Polish or Ukrainian separatism. This state policy dovetailed with the few Ruthenian national activists who sought greater national autonomy for the region. Further complicating this was that other nationalist activists claimed both the region and the Ruthenians as part of their own lost homeland. The dissolution of the Austro-Hungarian empire over the course of the First World War accelerated this process as Ukrainians, Slovaks, and Poles claimed that they had a historical and ethnic ties to this region of Galicia. As a relatively underdeveloped borderland area, Galicia could not push for its independence in the interwar period and often the definition of "Ruthenian" was up to whichever power controlled Galicia. For example, the Soviet victory in Eastern Europe resulted in the incorporation of this part of Galicia (the Transcarpathian Ukraine") into Ukraine SSR and treating the Ruthenians as a subgroup of Ukrainian. There was an attempt to replace the Ruthenian with Ukrainian under the Soviets and forcibly incorporated the Ruthenian church into the Russian Orthodox church. Despite these efforts, elements of Ruthenian culture and language have survived.

Sources

Hann, Christopher M., and Paul Robert Magocsi. Galicia: A Multicultured Land. Toronto: Univ. of Toronto Press, 2005.

Wolff, Larry. The Idea of Galicia: History and Fantasy in Habsburg Political Culture. Stanford, Calif: Stanford University Press, 2010.