that's morse taper tooling. it probably will fit your drill press. The chuck that is currently install likely has one of these morse taper arbors on it. The spindle should have slots on the side into which you can isert and angled drift to break the taper and remove the chuck, and install another MT shank tool.
Edit: you also have some MT sleeves (adapters) and a couple of dead centers there. The centers are for a lathe tailstock. Your other MT tooling can be used in the tailstock also.