I would like to know if the phrase "I've arrived by car" is grammatically correct, and if yes, what is the difference between this phrase and the phrase "I arrived by car".
Both are grammatically correct, but it is hard to think of a natural situation (i.e. one that isn't contrived) where you'd use the first, rather than the second. As @user3169 said, the first is present pefect - but I can't think why you'd want to tell some one in that moment "I have arrived by car". It's more likely that you'd be answering a question like: "how did you get here today?" to which you can quite naturally answer "I arrived by car."