Right now, there seems to be no definition of what the dates mean on copyright / phonographic copyright rels.
actually, there is. the year next to ℗ & © symbols denotes the "date of first publication"* (see note below). ℗ pertains to the sound recordings while © pertains to all "visually perceptible" elements of copies of a phonorecord (which can be any medium, including digital releases, containing the sound recordings).
from that year, the sound recordings and phonorecord copies enjoy a certain term of copyright protection. the number of years sound recordings enjoy this protection varies. the determination of the period is a bit tedious to figure out though. (incidentally, since Mar 1, 1989, copyrights notices have been optional; even if no copyrights notices are printed on releases since that date, those releases still enjoy copyright protection nonetheless.)
The 1976 Copyright Act defines publication as "distribution of copies or phonorecords of a work to the public by sale or other transfer of ownership, or by rental, lease, or lending." An offering to distribute copies or phonorecords to a group of persons for purposes of further distribution, public performance, or public display also constitutes publication.
as for whether one should add a closed or open date, it is a matter of interpretation. one could say that a particular release was first published in 2001, so ℗/© 2001 could denote the year an event took place, and a certain term of protection following that event is implicit. alternatively, one could also interpret the year as the start of that certain term of protection. what the latter approach does better though, is that sometimes you will encounter releases inadvertently giving different ℗ dates for the same recording(s), when a sound recording obviously cannot have more than one "date of first publication" event unless there are valid reasons*; otherwise, the clock starts ticking from the earliest date of publication. so reflecting copyrights as a span rather than as an event deals with this situation better when inconsistencies or ambiguities arise.
reasons for different "date of first publication" - remasters? different dates for different regions under different companies? copyright term extensions? i don't know if these count as valid.
© copyrights, by their nature, can only be attached to releases, since they protect all the "visually perceptible" elements of copies of a phonorecord, everything from artwork & photography to literature, everything except for the sound recordings, which are protected ℗ copyrights. as packaging can evolve, so too can © copyrights "date of first publication" change, while still embodying the same sound recordings as earlier iterations of a phonorecord.
That kinda breaks for cases like "(P) 2000 - 2001" though
that does not make sense. perhaps the editor misinterpreted info presented by the release. eg, in the compilation https://beta.musicbrainz.org/release/aeb57c3d-3cd4-4c19-9f95-e678e41b3610/ some recordings may have been first published in 1990 and others only later in 1997, so the compilation might have reflected that as "℗1990,1997 HNH International Ltd." (something you'll see practiced fairly often) to indicate different "first publication" dates for unspecified sound recordings contained in the compilation.
sorry about the length; i did try to trim it down.