One title can have several numbers
An ISBN is useful because 'the same book' can mean several things. A reader may mean the story. A bookseller may mean one publisher's paperback. A librarian may mean the copy with a damaged cover on a particular shelf. Those are different identification problems.
The International ISBN Agency says different language editions and different formats need separate ISBNs. A substantial revision also requires a new number. A price change alone does not. An unchanged reprint keeps the original ISBN when the publisher, text and binding remain the same.
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Track the publication and the copy
Bowker's ISBN guidance describes a reprint as additional copies without substantial changes, while a new edition has substantive alterations. It also distinguishes the identifiers for a multivolume set from those for volumes sold separately. This is why comparing titles alone can join records that should remain separate.
For a practical catalogue, make three fields explicit: the work being discussed, the publication being cited and the local copy being handled. Record the printed ISBN, publisher, edition statement and format together. Give a borrowed or donated copy its own inventory identifier rather than expecting its ISBN to distinguish it from every other copy.
What the number cannot promise
An identifier is not an assessment of accuracy, literary quality or condition. Nor does a matching number prove that a seller's description is correct. If a quotation depends on pagination or wording, inspect the edition itself. The catalogue should help someone find the evidence, while preserving enough detail to notice that they have found a different version.