Not really. What's more, the difference is getting smaller all the time. Textbooks and websites are full of lists, saying categorically 'X' is British English or 'Y' is US English, or 'the Americans say this' and 'the British say this'. This is very misleading. The language is changing at a very fast pace, and many of the differences are disappearing.
US English dominates the media, especially digital media, to a massive extent. In the UK, the younger generation are growing up using American vocabulary, expressions, constructions and in some cases even pronunciation without even being aware of it. Some Americans are adopting more traditionally British words and expressions, though to a far lesser extent. In a few decades' time, there may well be one global English.
All the varieties of English are mutually intelligible with each other. English speakers don't need to speak a "standard English" (not that there is such a thing) to speak with each other. The different varieties of English are really just different accents rather than dialects. Some vocabulary is different, which can cause confusion, but there are very few differences. You can usually read several pages of a book and have no idea which country the writer's from. This entire post is in Australian English, and if I didn't check his profile, I could've believed that Michael's post was too. I also get the impression that there are more generational differences than regional differences.
The biggest accental differences you'll find between different varieties of English are how the vowels are pronounced, how "t" is pronounced between two vowels, and how "r" is pronounced at the end of a word. Beyond those, the differences are mostly negligible.
If a U.S. speaker and a British speaker are talking to each other in a conversation, it is effortless. There's no problem in communicating.
I worked at a company that had some British managers and been in meeting rooms when U.S. and British colleagues were engaged in a spirited, interactive discussion, trying to decide on a course of action. There was no language barrier.
Sometimes there are subtle cultural differences, just as there are between different regions in the U.S.
A British speaker might intuitively choose a slightly different word or phrase than a U.S. speaker, but British usages are a comfortable, familiar part of U.S. passive vocabulary.
If I ask "Is Susan here?" and someone answers "She's just left," I don't have trouble understanding it. I don't think "that's wrong," or "that's strange," or "that's British." The sounds go into my mind and I understand "She just left." I don't even notice that it's different from what I'd say myself.
British professors teaching in U.S. universities typically make no attempt whatsoever to modify their speech. From time to time we hear a surprising difference in pronunciation, like <em>SIGH-napse</em> instead of <em>SIN-apse</em> (for <em>synapse</em>), <em>SHED-y'l</em> instead of <em>SKED-jule</em> (for <em>schedule</em>), <em>vittamins</em> instead of <em>vyteamins</em> (for <em>vitamins</em>) and shrug them off, just the way we might shrug off a regional difference within the U.S. (<em>pop</em> for <em>soda</em>).
No, not really.
There are differences in slang, verbiage, and accents, but people from the UK and Ireland and the United States are able to understand each other pretty well with the exception of some extreme cases.
Just to add to what others have said, the younger generations in English native speaking nations are quite quicky adopting the same speech patterns, accents, vocabulary, and behaviours. Considering how quickly this process is happening I don't see them as being British, American, Australian etc. In fact, I just see them as young westerners.
Strangely, when I speak to young Spaniards and they have the courage to speak some English to me, they also seem to be part of this cultural group, and try very hard to sound just like their native English counterparts.
