The differences are less noticeable in colloquial British speaking where the American version is often used.
The British versions are more to do with the way it is taught in classrooms and in the official language teaching text books of the British.
It is all just English if you know English you can communicate with other English speakers. You may find some phrasing sounds different to your preferred dialect. But it is still English, if you know what the other speaker means why argue over nothing. Does not apply to slang or some words that may be offensive between the different English speaking continents.
Thank you all for your comments...
Leyla asked " I would like to know your opinion about American and British English? In your mind which of them must we prefer?:)"
As an older Canadian, I learned British English in school and learned American English from newspapers, advertising, movies, music, radio and TV.
I cannot say that I prefer one form over the other. I like them both and Canadians know both forms of English.
So, I don't care if someone spells color or colour, defence or defense or says elevator or lift.
I do have a small preference for some American spellings because they seem to make more sense phonetically, for example, I prefer recognize (AmE) and analyze (AmE) but the other spellings are also OK.
In conclusion, in my case, I am comfortable with both forms of grammar and spelling.