Well in JIRA, archiving simply means that you're making that item (project, versions, etc) no longer accessible. The data will still exist, but is no longer used until it's unarchived.
Deleting means that you're completely removing that data. It will no longer exist in JIRA's database. There is no way to recover that data without a backup file.
This also explains project archiving a bit:
In the past, Portfolio for Jira required a high degree of detail–foresight that was unrealistic for many businesses to have–in order to produce a reliable long-term roadmap. We're tur...
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