Does the term "Asian" have different meanings among various English-speaking countries?

Asia is everywhere from the Caucus mountains to Australia - including the middle east, India, China and Siberia.

There is a difference in common usage, in AE it seems to imply China/south-east Asia more than India. While in BE 'asian' would be more likely to refer to someone Indian/Pakistani.

I'm guessing it's mostly just the relative populations of each group in Britain and America.

Here in Britain, in my experience Asian commonly refers to people from the Indian subcontinent, more so than people from the far-east. I'm sorry I don't have any citations to back this up though. If anyone has any, I'd be happy to add them here.

Like all questions dealing with complex issues, the answer is very simple; it depends.

Geographically, any resident of the Asian continent, which is historically bordered by the Ural Mountains and Red Sea on its west side and by oceans to the north, east and south, is an "Asian"; they are a person of Asia.

However, in more common parlance the term tends to exclude Russia, what we currently call the "Middle East" including Pakistan, and the countries in the "Indian sub-continent" including India proper and other nations to the southwest of or in the Himalayan range such as Nepal, Bhutan, etc. This leaves primarily Mongolia, China, Southeast Asia, Japan, the Indonesian archipelago and most other Western Pacific Islands besides the Australasian islands.

This was not always so, especially in terms of India; during British colonial days, the Indian people and those in neighboring territories were termed "Asians". The two terms were at one point roughly synonymous, as the entire region from the Horn of Africa to Southeast Asia was once known as the "East Indies".

Strictly speaking Asian means anything related to Asia. A good reference for these boundaries is Wikipedia:

Other terms related to the area include Oriental, Far East and so on. These tend to refer more directly to the associated cultures of Asia, however, and typically do not extend very far north. For instance, Russia and the surrounding area is not considered Oriental. But these terms are also somewhat varied and I again recommend Wikipedia to help clarify any questions.