I would add something to what Svätoslava has written:
Národ (nation) in Slovak has meaning almost identical to Greek "ethnos". A group of people with some common culture, language, consciousness.
Nemzet, ság or nép (nation) in Hungarian means "state/country" or "all people who live in a state", like in English. see edit below
This difference does much.
There has been no Slovakia as a country/state before 20th century, Slovakia is simply not a historical country.
Therefore, from historical point of view, it is not a country, only a newly created state.
From Hungarian point of view: no Slovak country had ever existed before 20th c. = no Slovak nation (nép/ság/nemzet) had ever existed before 20th c.
From Slovak point of view: no Slovak country had ever existed before 20th c. = Slovak nation (národ) could have existed regardless of this.
I think the Slovak concept of národ is inspired by Johann Gottfried Herder. If I remember well. I try to search.
EDIT: I think that instead of nemzet the right word in Hungarian for this concept should be ság or nép (šág/nýp). I am still not sure, though.
About Herder and nation:
I link a document for Slovak Studies at Pittsburgh University:
I cannot quote because the document is protected.
edit2: One more quote about Herder from Wikipedia:
"He [Herder] also predicted that Slavic nations would one day be the real power in Europe, as the western Europeans would reject Christianity, and thus rot away, and saying that the eastern European nations would stick to their religion and their idealism; and would this way become the power in Europe. One of his related predictions was that the Hungarian nation would disappear and become assimilated by surrounding Slavic peoples; this prophecy caused considerable uproar in Hungary and is widely cited to this day."