Cheap drill press with cheap chuck. I doubt that either has a means of adjustment. I've never seen gibs on a drill press. Some have split heads, some have an adjustable screw to hold slack to one side, really cheap ones, nothing. Go to the store and check them out. You won't be able to run it but you can chuck something and see how close & far it moves from a block put on the table. Only buy the floor model you check.
I've had 4 drill presses, all bought new. #1. bottom of the line Craftsman in the '70s, No adjustment very quickly developed too much slack. #2. "Commercial" model Craftsman, '70s Split head with adjustment, decent chuck, still have it. #3 Jet bench model, 70's adjusting screw on the side of the head, crappy chuck, replaced, OK machine, still have it. 2010, #4, 20" Grizzly floor standing model, really poor quality, the return spring broke twice and took months to get new ones from Grizzly, the stop was a flimsy piece of soft metal, the runout was excessive, sold it after 2 years.