There are various unclear parts in your Q, but if it is why Slovakia's parliament (probably) voted less enthusiastically on the latest NATO expansion is that the population is nearly as pro-Russia as Hungary is (nowadays).
Most Slovaks want Russia to win Ukraine war
The representative survey named “How are you Slovakia?” has been conducted by MNFORCE and Seesame agencies and the Slovak Academy of Sciences. Those surveyed had to respond to the survey using a 10-point scale, according to which 1 means a clear victory for Russia and 10 for Ukraine.
Approximately a fifth of respondents said they wish for a clear victory for Russia, with more than half saying they are inclined toward a Russian win. Meanwhile, only a third said they tended towards Ukraine, and only 18% expressed no preference.
Divisions are clearly noticeable on the party level. For example, the overwhelming majority of voters of the SMER-SD of former Prime Minister Robert Fico are on the Russian side. [...]
Regarding the geographical differences, only the population of Bratislava has a majority of people wishing for Ukraine to win. [...]
In February 2022, before the invasion, 44% of people blamed NATO and the US for the tension on the Ukrainian borders, while only 33% blamed Russia.
Regarding NATO membership, only 45% supported it in the survey from 2021. Right after the invasion, support has risen, but it has started to decline again recently.
And their own NATO politics are a bit strange too...
The Russian invasion of Ukraine also came amid a tortuous debate about Slovakia’s place in NATO.. After years of argument, Bratislava finally signed a Defense Cooperation Agreement (DCA) with the United States in early February.
For its critics, it spells the end of Slovakian sovereignty. Robert Fico, a former prime minister, called it “treason”, despite himself starting the process when in government.
And a bit like Orban, Fico has condemned the Russian invasion but is opposed to economic sanctions on Russia.
One Slovakian website says it was mainly the far-right which opposed the NATO expansion in parliament
As many as 126 MPs of 143 present MPs voted for Finland’s accession to the Alliance. Regarding Sweden, 124 of 144 present MPs supported the country’s decision to join NATO on September 27.
In addition to several MPs from different political parties, far-right MPs voted against the protocols en bloc.
So that would give 17-20 oppose or abstention votes (source isn't too clear on that), so that would not be Fico's party, which is socialist. The DCA with the US, back in Feb, faced a tighter vote though 79-60. From another article on those protests, it seem the far-right party which opposed both is People’s Party Our Slovakia, but they only have 7 votes in parliament nowadays. On the other hand they have 2021 splinter group in the The Republic, which also seems to have voted against, according to Euractiv:
Only members of the far-right parties People’s Party Our Slovakia and The Republic voted against it.
Interestingly, accession has been supported also by members of the SMER party of former Prime Minister Robert Fico. SMER sees the conflict in Ukraine differently than the official Slovak position.
According to Wikipedia, People's Party Our Slovakia won 17 seats in the 2020 election, but suffered several defections including that 5-seat new party splinter in the aftermath. Seemingly that was due mainly to disagreements over the party leader's powers rather than other policy.
