I'm afraid I don't understand your problem.
The term "Asian" is usually used (particularly in the USA) as a racial term indicating the peoples previously known as oriental. Thus Chinese, Japanese, Korean, Vietnamese, etc.
In recent years however the term has been used (or "South Asian") to refer to Indians, Pakistanis, Iranians, Afghans, and others.
This categorization fails in my opinion on a number of fronts:
1) Racial: These are different ethnic groups, primarily caucazoid.
2) Geographic: Contiguous land mass doesn't separate Asia from Europe so the division is apparently arbitrary.
3) Plate tectonics: India is on a separate plate from the rest of Europe and what was previously known as Asia; it's on the Indo-Australian plate; with respect to plate tectonics you could even call it a separate continent that just happens to be jammed into Eurasia.
I think it would be clearer and more consistent to speak of the ethnicities as being Asian and Indian (separated) rather than collectively Asian and to refer to the geography as "Asia and the Indian Subcontinent."