What differs between post-filter and global aggregation for faceted search?

To do 'faceted search' or 'faceted navigation', we can both use post-filters or a global aggregation to get counts for results "outside" the actual resultset we want to show.
I wonder why both options are there, what the difference is, etc; they look to provide the exact same features in a somewhat different way.

Complete question, including some examples and references here:

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