I think it *was* 3/8"-16... I had some holes in aluminum that I boogered up. I took a piece of scrap steel, drilled a hole, tapped threads, tried the set screw. It fit perfectly. So I used that size tap to clean up the threads in the aluminum pulley. After I did that, it was painfully obvious that I had used the wrong tap. The threads were now *seriously* loose, though the set screw did fit.
I ended up drilling it out one more size and cutting new American threads for an American set screw, the way the woodworking gods intended. Metric is for sissies and Kanukistanis.
I'd bet 13.5 cents that the threads in your drill press are Metric. You probably don't want to repeat my screw-up, though anyway it might have been
1/4"-20 or 5/16"-18... I can't quite remember. Whatever it was, the metric screw fit well enough into the American threads. Just didn't get solidly tight.