For a long time, linguists called Czech and Slovak the same language. The reason was many Slovaks could communicate with many Czechs, and vice versa.

When Slovaks asserted some degree of autonomy (staring in 1840s), they put pressure on the linguist field to claim that Slovak was a unique language. And eventually that became common and academic knowledge. Slovak was deemed different enough from Czech to warrant official status. But from what you saying, that difference might be smaller than dialects in Denmark.

My father was born in Slovakia. I was always amazed at how he could converse with Czechs, Poles, and Ukrainians. Maybe not a full understanding, but causal conversations and simple instructions were possible.

Slovak is regarded as the closest descendant of the Old Slavonic, the mother of the Slavic languages. Slovaks were oppressed by Hungarians for centuries, but the upper class language did not influence the lower class language that much. In that way, more of the Old Slavonic was retained in Slovak as compared to the other Slavic languages.

Both Czech and Slovak have their regional dialects. In northwest Slovakia, there is a region called "Zahoria." THey speak a dialect that is 3/4 Slovak and 1/4 Czech.

I spent one year in Czechia. I studied standard Czech, but I did not gain enough skills to recognize the dialects. Then I spent one year in Slovakia, and I studied standard Slovak, and I gained enough skills to converse on a simple level. But the city I was living in was not speaking standard Slovak, but I quickly picked up on the differences. Going to a different city required a different adaptation, and I was able to adjust fairly quickly. But I didn't go to eastern Slovakia, where, from what I heard, have a significantly different vocabulary than the western and central dialects.