The Hungarian language is totally different to the dialects spoken by its neighbours, which usually speak Indo-European languages. Hungarian comes from the Uralic region of Asia and belongs to the Finno-Ugric language group, meaning its closest relatives are actually Finnish and Estonian, which are two other really difficult languages for foreigners to learn because they are pretty alien compared to any other languages.

I'm guessing the words you mentioned are all close because they are modern. In the same way that many words that have entered Japanese in the last 200 years are actually English or Portuguese words brought in by foreigners and adapted to the local pronunciation. You can cheat so much in Japanese by simply learning to read katakana and finding all the English words.