Thanks, Dale. I tried this, and yes, I got the same result using the 'Geodesic" method when using the Buffer tool/Select by Intersect tools and then just a Select Within a Distance tool.
But when BOTH tools are set to Planar (Euclidean), I get different results. ...Why?
...By the way, the Input points are in projected coordinates (UTM), and the Distance used is 500 feet.