Columbia Records (EMI-owned 1931-1990, worldwide except US, CA, MX, ES, & JP; largely defunct since Jan 1973)
Worldwide catalog numbers used by Columbia Records: https://rateyourmusic.com/wiki/Music:Columbia+(EMI)
Releases in all countries (except the US, CA, MX, ES, and JP) between 1931–1990 that bear the word mark "Columbia" should belong to this label*. US and CA releases from 1931–1990, and all pre-1931, and post-1990 releases except those from JP, and post-2004 releases from ES, should belong under Columbia* (see exceptions and other notes at bottom).
Columbia Records (featuring the "magic notes" logo) was a worldwide imprint owned by EMI outside of the US/CA/MX/ES/JP from 1931–1990*.
(* EMI Group replaced it on Jan 1, 1973 with its newly-launched EMI imprint, and Columbia Records became largely dormant from then till Sony Corporation completed its acquisition of the rights to its use from EMI, and launched its own Columbia brand globally on Jan 1, 1991.)
The Columbia Graphophone Company, as it was then known before 1931, was originally the UK subsidiary of the US-based Columbia Phonograph Company, which the latter sold off in 1922. Sometime between 1925–1929, Columbia Graphophone acquired its former parent.
In 1931, the Gramophone Company and the Columbia Graphophone Company merged to form Electric and Musical Industries (EMI). American anti-trust laws forced EMI to sell off its US-based Columbia operations.
Until 1951, EMI-owned Columbia's output was mainly recordings licensed from American Columbia, when the latter switched British distribution to Philips Records.
Until 1968, EMI Columbia continued to distribute American Columbia sister labels OKeh and Epic when American Columbia's then parent CBS Inc. moved distribution of all its labels to its new-formed subsidiary CBS Records Inc. (Since 1961, CBS, Inc. had already begun releasing Columbia recordings under the "CBS" imprint outside of the US and Canada. Then in 1966, it created the separate subsidiary to manage both the "Columbia" and "CBS" labels.)
On Jan 1, 1973, EMI replaced the Columbia label with the recently-formed EMI Records, to avoid confusion with the US-based Columbia label. While it had ceased to be an active label by then, the Columbia name remained in use on some EMI releases between 1973–1990.
By 1988, Sony had already acquired Columbia along with its parent CBS Records Group. As CBS had only granted Sony a temporary license for the use of the CBS Records name outside of the US and CA, Sony eventually acquired the rights to the Columbia trademark (aside from the US, CA, JP and (until 2004, when it acquired the rights there) Spain, which were still owned by EMI, allowing Sony to use the name as a worldwide imprint. In Japan, the name is owned by an unrelated company, Nippon Columbia.
* exceptional cases: EMI had engaged in litigation with CBS regarding the import of US releases bearing the Columbia word mark into countries where EMI had still owned the rights to the name at the time. this may explain the existence of non-US releases with the Columbia label prior to 1991 (after EMI had sold the rights to the name to Sony), when rightfully they shouldn't.
where do pre-1931 releases go?
for US releases, the logical label to use would be the Columbia Phonograph Company (predecessor of the present-day Sony-owned Columbia.
for UK or other non-US releases, the logical label would be its British subsidiary then, the Columbia Graphophone Company (predecessor of this label, EMI-owned Columbia Records)