Usually this occurs after the original issue has been out of print for a while. For instance, if that particular recording had been paired up with another recording when Columbia brought out double sided discs in 1908, that would qualify as a reissue.But copies of a double disc Columbia issued in 1908 that remained in the catalog through the end of the acoustic era in 1925 would all be considered the same issue, though collectors will run across pressings reflecting three significantly different label designs and many, many more sub variations of each of those three designs.So, if I understand it correctly, while my record dates from 1905-1906 the recording it features is indeed from 1901, but this particular record is a reissue? Had the Columbia label design not changed, there would be no way of being able to date the pressing.A reissue is when a recording is brought out under a different catalog number or even on a entirely different record label.
And the major record labels also issued recordings overseas though their foreign affiliates.Usually, from a collecting standpoint, a label reflecting an early pressing is considered more desirable. It wouldn't surprise me, in fact, if there are collectors, who attempt to pick up copies of various favorite records reflecting the various label designs - and some of those label designs will be harder to find than others.