Visited Ukraine (Kyiv) last summer. I spoke a little Russian with them; nobody seemed to mind.

Honest question from a less than A1 level Russian student... Is there really a significant difference between the two? I have no doubt that there is different vocabulary etc. and of course that there are political reasons to count them as different languages but are they effectively mutually intelligible?

Russians often claim that Ukrainian is totally mutually intelligible, but it is easy to find counterexamples. There are Taras Shevchenko poems, for example, that if you present them to the average Russian speaker, that Russian speaker would have to guess at the meaning of a large number of words (and would guess wrong). All of the Slavic languages have retained common features and two speakers of different Slavic languages can often drop to a sort of basic shared level to communicate, but the innovations in each language – especially with the rise of complex standard languages – should not be underestimated.

Even within Ukraine, Ukrainians from Kyiv can face some difficulties understanding the Ukrainian spoken in the Carpathians (which is either transitional to Rusyn or is actually straight-up Rusyn), or the rural dialect of Trans-Carpathia that can include a great deal of Hungarian words.

I have an anecdote. I speak Russian proficiently (I can speak it since I've been 6, even though my native language is Romanian), and I always found understanding Ukrainian hard (not to say speaking it). I can infer a lot of words and expressions, but I would say they're fairly different.

You can try it out for yourself -- listen to some Okean Elzy on your favorite streaming service and see if you can understand him. (For all other non-Russian, non-Ukrainian speakers, the music is pretty good either way :))

I'm a Russian speaker who listens to Okean Elzy and I heartily give this suggestion a thumbs up.

I was surprised when a normally-Russian-speaking Ukrainian colleague of mine mixed up months when trying to communicate in Ukrainian with another normally-Ukrainian-speaking Ukrainian - talking about something occurring in October but using "Listopad" (which I figured from Czech was actually November). I'd guess that there's enough similarities that you could have a reasonable conversation with someone when you know Russian and the other speaks Ukrainian ... but occasionally you'll encounter words which are just completely unintelligible and not even close.

Listopad is a Ukrainian word for October

I just double checked and it seems everywhere I look lists Listopad as meaning November, with October apparently being “Жовтень”. However there are a bunch of other Slavic languages which DO have October as something like Listopad (https://en.m.wikipedia.org/wiki/Slavic_calendar) so perhaps I shouldn’t be so sure of myself in future :-)

A friend of mine from Lviv tells me that Ukrainian language is closer in structure and vocabulary to Polish than to Russian. I can't really assess this information, as I speak only Polish, from these three.

I always heard the same, but I'm no linguist and know nothing of Polish or Ukrainian so it would be good to have native speakers to confirm.

That's right, but only few people speak pure Ukranian language (and they do it mainly for political reasons). It is incovinient as it lacks some modern words and concepts. One can discuss prices on the market or neighbor girl, but when topic is switched to scientific or ingeneering matter - Russian is language of choise. Same with Kazakh language - the language of nomads.

Confirm: Ukrainian is perceived by russians as "peasant's" language. As for scientific and engineering matter - I observe more use of words borrowed from English.