You are wrong about phrasal verbs... British English uses phrasal verbs all the time. In the example you give the difference would be informal vs. formal. As Jonathan says, there are a number of word variations between American and British English. But these are quickly learnt and do not pose any real problems of communication. In any case, in the UK we watch so much American TV and films, the variation in words soon becomes interchangeable - especially for younger generations.

There are numerous small differences. Brits say "lorry" when we say "truck." What we call "eggplant" they call "aubergines." Perform a search for "US English vs. British English" to see more examples.

There are so many small differences. I grew up speaking British English but my mom's side of the family is from the USA. The biggest difference in my opinion is the accents but there's also different vocabulary, phrases, idioms, spelling etc. They even say there numbers differently for me example... In the USA 1200 is one thousand two hundred and in the UK it's twelve hundred.

Notice that the Wikipedia I cited links to two other articles: "Glossary of American terms not widely used in the United Kingdom" https://en.wikipedia.org/wiki/Glossary_of_American_terms_not_widely_used_in_the_United_Kingdom and "Glossary of British terms not widely used in the United States." https://en.wikipedia.org/wiki/Glossary_of_British_terms_not_widely_used_in_the_United_States These cover the VERY RARE cases where someone in one might country might not understand a word used in the other.

No matter where you go in the language world, there are differences in the way people speak or express things in a particular language. For example, Spanish is a language spoken by many people in many different countries and the same object can have several different names depending on where you are. The same exists in English and I imagine in Russian as well. For example, I'm from the northern Midwest of the U.S. and here we say "bag" but in Indiana, in the southern portion of the Midwest, they call it a "sack". We all know both words, but in my region, "bag" is the more common word to use for the thing you use to carry your food home from the supermarket. If someone says "sack" to me, I'm going to think of a huge, scratchy bag that holds coffee or rice, not a plastic bag I would get at the supermarket. Within my home state, we have different terms for different items and we can identify where a person is from based on that. As Charlie said, there is so much television available around the English-speaking world that all of us can easily learn the different terms through context, social media, or dictionaries that most of us are familiar with the basic differences. So, yes there are differences in vocabulary, slang, idioms, etc., but no more than can be expected from any other language that is spoken by many people living in many different regions.