https://sjp.pwn.pl/slowniki/trucizna.html
The point is, both are correct(afaik) while in English venom and poison are definitely two different things.
No? That's how I've always said it. "Ta żmija jest trująca" - don't see any issue here. Jadowity grzyb I'll agree.
You've never visited Italy ? They're not that far away and I'm sure you'll love it.
No, the situation in English matches your description exactly: all of these things are called poison. The word venom is almost never used in natural speech.
Furthermore, if you ask English speakers what the difference between poison and venom is, by far the two most common responses will be "there isn't one" and "I don't know". icyfox is just looking to be annoying.
(Another popular option will probably be "it's called venom when you're talking about snakes", which explains roughly 100% of use of venom in natural speech.)