The term "Asian" is definitely a geographic one, even though people tend to associate it with ethnic groups/nationalities.
For example, I was rather surprised to know(when I was a new immigrant here) that the term "Asian" referred to East/South East Asians in north America. In the rest of the English speaking world, Asian usually means anyone from the Asian continent.
I believe that historical migratory patterns have something to do with how the term "Asian" came to be associated with East/south East Asians in America. My theory is that the first "Asians" most Americans first met were the Chinese who migrated to the west coast in the 1800s. I do not think there were any other Asian groups present in North America in signification numbers at that time. Thus Asian=Chinese/East Asian became the norm. In England, to this day the term "Asian" means "Indian/someone form the Subcontinent". This is due to the fact that English probably had more ties with those from the subcontinent than they had with east Asians. East Asians in England/Europe are referred to as the Orientals. These differences lead to some rather funny misunderstandings
Oh btw
While most of the south east Asian/East Asian languages do not have much similarities, there are some fundamental similarities when it comes to script. For example, Cambodian, Thai, Burmese and Laotian languages use the same script/have a script that has a common origin in India. In fact the script I use for my language (Tamil language) is also a sister script to the aforementioned south east Asian scripts. They have the south Indian Pallava script as the parent script.
Imho Asians are more related (Linguistically/culturally) than it might appear at the start, even though we are very diverse ethnically.