In fact, those two nations are not connected much, even if their flags, coats of arms and names are remarkably similar.
They are both Slavic nations, and this is what the name implies. But Slovaks are part of West Slavic group (that includes Czechs, Poles and Luzatian Serbs, among others), while Slovenes belong into South Slavic group (with all the nations from former Yugoslavia and Bulgarians).
The etymological source of the name comes from old Slavic word "slovo" meaning "the word" and also "a man." Sloven (or Slovan) was literally a man, whose words you could understand. In contrast, the man, that couldn't be understood was called "Nemec" - the mute one. And this is still the word for Germans in (I believe) all Slavic languages.
The Slovene and Slovak languages might sound very similar to a foreign ear, with plenty of same sounding words, but they might have a totally different meanings. Consequentially, Slovenes and Slovaks do NOT understand each other, when both speaking in native language. They may lead some really basic communication (like asking for directions) that would include a lot of pointing and body language. On the other hand, Slovaks have little problem communicating with Czechs and Poles, and Slovenes can converse with Croats and Serbs, but not Bulgarians or Macedonians:)
Other than that, the countries are remarkably similar, with plenty of forests, nature resorts, spas and castles. The city architecture is also very similar, with main influences being Habsburg empire and later socialist regimes. Both are proud of their beers and wines, but unlike Slovakia, Slovenia has some coast at the Adriatic Sea. Oh, I almost forgot: Slovakia is twice the size of Slovenia and has around 5 million inhabitants (Slovenia: ~2 million)
All in all, it is no wonder that those two nations are so easily confused. and at the 2014 Sochi Olympics hockey turnament, both countries played in the same preliminary group, along Russia and USA. I can imagine American players wondering, why they need to play twice against the same team :D Well, they have beaten us both, yet we Slovenians still managed to historically qualify for quarterfinals:D