Before World War I, Slovakia, parts of Poland and the Ukraine were considered parts of Hungary's Upper Kingdom, in the Austro-Hungarian Empire. Many immigrants found on this website gave their country of origin as being Hungary, Austria, Poland, Austria/Hungary, Galicia, Bohemia or Morovia, the later two forming the current Czech Republic. Below is an explanation of how Slovak, Czech and Ruthenian ethnicity survived through the formation of Czechoslovakia, Slokavia and the Czech Republic. It was written by Bill Tarkulich, an excellent eastern european genealogist, his site has a link, on the home page. None better, anywhere.
"Slovak" and "Czech" describe specific ethno-linguistic peoples. Each has a unique language and is described as it's own ethnicity.
I would not use "Slovak" to describe the people of Upper Hungary, since italso included the ethno-linguistic Ruthenian (nowdays called "Rusyn")people. It is fair however to say, that the dominant ethnicity of Upper Hungary and today's Slovakia is Slovak. Some people today casually use Slovak to refer to this region but this is not entirely accurate.
The first Czechoslovakia was an unhappy marriage between these three ethnicities. The Ruthenes extended from Eastern Slovakia, deep into Western Ukraine in the first formulation ("TransCarpathia"). Each of them wanted their own country.
After WW2, the Slovaks again tried to get their own nation-state, but lost out. During the second Czechoslovakia, the Czech culture dominated interms of wealth, politics and resources, leaving the Slovaks and Ruthenes feeling as second-class citizens. When they finally had the opportunity in 1993, they separated over cultural differences. One could argue that has left Slovakia the poorer of the two states.
With regard to churches, the Ruthenes stuck with the Greek Catholic church, while the Slovaks were distributed between Roman Catholicism and the various Protestant religions. Under Communism, all churches except the Greek Catholic were free to operate, but attendees were heavily discriminated against. The communists even went so far as to elliminate Ruthenian as an ethnicity and dissolved the Greek Catholic Church. This led to a real confusion and misrepresentation about what ethnicities existed. You'll see this as you look through the 1950 to 1990 census of Slovakia, and then look at a modern-day census. All of a sudden, people "changed" ethnicity and church affiliations, so be careful as you examine the data.