The distinction between British and American English is not as strict as foreign learners are led to believe. In the case of movie/film ( 'the next Bond movie'/'the next Bond film') or movies/cinema ( 'going to the movies'/ 'going to the cinema'), I can assure you that all native English speakers are familiar with both words. In fact, both words are used on both sides of the Atlantic. An American may well use 'cinema' to talk about the genre, or to refer to a more artistic, European-style production. Meanwhile, British people often use 'movie' in an informal context, especially to talk about a more commercial blockbuster production. Australians tend to use them interchangeably. Unlike early films, the distinction between AE and BE is never 'black and white', as they say (!). Foreign learners are often given very misleading lists of words with a big line down the middle, with 'American' on one side and 'British' on the other, implying that there is an unbreachable divide between the two forms of English. In fact, this is not the case at all. As with film/movie/cinema, it is more a question of preference and frequency of use, together with subtle shades of meaning. Usage depends on the context, the age of the speaker and many other factors. What's more, it's changing all the time. Many usages which would have been on the AE side of the line are now widespread in the UK, especially among younger people. As for the IELTS exam, I can also assure you that you will never be penalised for using an American word, phrase or spelling. The markschemes for IELTS take American English into account.

Both are correct and indeed they both mean the same thing, but 'the movies' is probably considered more colloquial than 'the cinema'. The term 'movies' is a shortened form of 'moving pictures'. Any British person would have no problem understanding you, and indeed a lot probably say 'movies' themselves. I see no why reason why it would be a problem in IELTS either. Film and movie are likewise interchangeable. 'Film' refers to the actual physical roll of film that 'movies' used to be recorded with.

Hi, as an alternative answer (beside to the American or British English issue) I'd simply say it deals on a Figure of Speech: here "the movies" stands for "the place where the movies are shown"(that is "the cinema"). In Linguistic this is called "Metonymy" (https://en.wikipedia.org/wiki/Metonymy) as for example "To go to the altar" means "Marrying in the church".