It doesn't seem to be impossible that someone could qualify for both, but the requirements are quite a bit different.
For example, for the real property tax credit, your residence can't have been completely exempted from real property taxes. But to qualify for the real property tax relief credit, you must have "owned and primarily resided for six months or more of the tax year in real property that received the STAR exemption or that qualified you for the STAR credit."
@az148
