Tricky to explain. Virtually all the 45s I have left (very few) have the small, spindle sized hole. In the UK we would play them with the same spindle as for a 33 rpm LP. Later on we started to see them with the circular central section held on by three or four lands so it could be easily punched out. The major advantage of that larger hole was in juke-box utilisation. The two can be made interchangeable by either fitting a "spider" adapter to each 45 rpm record or fitting an adapter to the player spindle. Something from Wikipedia:
"RCA 45s were also adapted to the smaller spindle of an LP player with a plastic snap-in insert known as a "spider". These inserts, commissioned by RCA president David Sarnoff and invented by Thomas Hutchison, were prevalent starting in the 1960s, selling in the tens of millions per year during the 45 rpm heyday. In countries outside of the U.S., 45s often had the smaller album-sized holes, e.g., Australia and New Zealand, or as in the United Kingdom, especially before the 1970s, the disc had a small hole within a circular central section held only by three or four "lands" so that it could be easily punched out if desired (typically for use in jukeboxes)."