Great question. There are a few reasons. First, take a look at the "Time Track" for each archive. I suspect you will find the Twitter Search API goes back in time, while the Twitter's PowerTrack (formerly Gnip PowerTrack) is roughly day-forward form the time you started the collection.
Next, try running a simple search for the key term used in the query against each API. Note the total results for the Search API. It should be lower than the total number of items in the archive. The reason here is that the Twitter search API matches on metadata, including the presence of the search term in URLs, which can be significant. You can do this as well using Gnip PowerTrack rules, but by default you only search Tweet text.
By diving into the data collected and using the various search, filtering, and visualization tools at your disposal, you should be able to discover other facets of the respective APIs.
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