When we clone issues in e.g. the 'Clones an issue, and links' post function, we handle the copying of most custom fields by simply getting the value from the original issue object and setting it in the new issue object. However, if the two issues are in different contexts for a given select-type field, then the Option values we get from the original issue will have entirely different backend IDs from those which are valid for the new issue, even if their display text might be the same.
It seems likely in practice that most users would consider two options with identical text, configured on the same field, to be one and the same from a domain perspective, even if Jira itself considers them distinct because they're in different contexts. Thus it would make sense when copying such a field to get the display text of whatever Option it contains, and use that to look up the appropriate Option in the context of the new issue. In principle this is a sound approach because no two options in the same context can have the same text, so there should never be ambiguity over which one to choose.