If a non-immigrant visa holder inside the US applies for ITIN and gets it, would he/she be considered as a non-resident or resident alien in the US?
Whether a person has an ITIN and/or an SSN has no bearing on whether they are a resident alien or nonresident alien for US tax purposes. A person is a resident alien if and only if they pass the Substantial Presence Test or the Green Card Test (or, in certain situations, if they elect the First-Year Choice, or a nonresident spouse elects to file jointly with a resident or citizen spouse).
The ITIN is intended for persons who have certain tax obligations, or reporting requirements, but are not eligible to a SSN. Plenty of foreigners have got an ITIN for example because they have to fill out W-8BEN forms relating to revenue accrued in the US.
Here is some more information outlining the SSN eligibility criteria: Social Security Numbers for Noncitizens
If you are authorized to work in the United States you might be entitled to a SSN.