In the book Doing research in the real world by David E. Gray, there is a section on experiment design. When discussing validity and reliability, the author defines “criterion validity” as
This is where we compare how people have answered a new measure of a concept, with existing, widely accepted measures of a concept.
and a little later, in the “Reliability” part, there is a subheading “Equivalence”, which says
Another way of testing the reliability of an instrument is by comparing the responses of a set of subjects with responses made by the same set of subjects on another instrument (preferably on the same day).
So if I got this right, we are both times measuring if there is a difference between the answer on our new instrument and another, existing instrument.
Is there a practical difference between the two concepts, or only a philosophical one? And whether practical or philosophical, what is the actual difference?
Update The author discusses validity and reliability in general, then lists 7 different aspects of validity and 5 different aspects of reliability. "Criterion validity" and "reliability equivalence" are only one type of each, respectively. Please consider in your answer that this question is not about validity vs. reliability in general, but only about these two specific aspects.