And here are some examples:
Hung. kéz (hand) = Finn. käsi, Hung. vér (blood) = Finn. veri, Hung. méz (honey) = Finn. mesi, Hung. szarv (horn) = Finn. sarvi, Hung. vaj (butter) = Finn. voi, Hung. eleven (alive) = Finn. elävä, Hung. menni (to go) = Finn. mennä, Hung. reped (to be torn) = Finn. repeää.
Then you have switches from h to k, as in Hung. hal (fish) = Finn. kala
Then you have switches from f to p, as in fej (head) = Finn. pää, Hung. fészek (nest) = Finn. pesä
Or, the letter n in Finnish is often replaced by ny in Hungarian, as in Finn. niellä (swallow) = Hung. nyelni, Finn. miniä (daughter-in-law) = Hung. meny
Hungarian and Finnish diverged 4500 years ago, and they represent the opposite spectrum of the Ugro-Finn language group. There are 9 languages in the same language group, and the middle parts of it have more in common with both languages than Hungarian with Finnish.
> Finnish is hard just because it's too different from our Indo-European languages mental model.
I'd imagine having this experience sure helps. Lots of people struggle to give up relying on mental translations to/from thoughts in their first languages.
Yes, there are grammatical similarities, no that won't help you much at all in understanding or talking to people...