Does кіно mean both a cinema (where you watch movies) and a movie (what you watch at the cinema)?
Кіно is a movie and a short for кінотеатр, which means "cinema" or literally "movie theater" (kind of like people say "movies") :)
Thank you. :) So without context I can't know whether that means "I like the movie" or "I like cinema" then?
Actually you are not likely to confuse those. You use кіно in the meaning of movies in the phrases like: Я ходив у кіно (I went to the movies), Ходімо у кіно! (Let's go to the movies), Я у кіно зараз (I am at the movies now). But you don't use to speak about some specific cinema, it's only Кінотеатр "Київ" (cinema "Kyiv"), У місті збудували новий кінотеатр (A new cinema have been builg in the city), Мені подобається цей кінотеатр (I like this cinema).
For "movie" we also have фільм and, although they can be intrchageable sometimes, there's a difference. Кіно is uncountable, фільм isn't (pl. фільми). You can use кіно to speak about movies in general. "Cinema" here does not mean a movie theater, but "the cinema, motion pictures collectively, as an art". Кіно is a word we usually use to speak about the art, about genres. You can say документальне кіно or документальний фільм (documentary film), but the genre is only "документальне кіно" (the same is true for other genres). So we tend to use "кіно' in a more art context