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If there is no Sphinx API for the language you are using SphinxSE allows you to do searches through MySQL.
If you are doing background processing and storing the search results in your database SphinxSE allows you to move the data from the searchd service directly into MySQL instead of going through an application layer.
You have to compile SphinxSE into MySQL.
Using SphinxSE requires some additional setup besides the basic searchd and indexer configuration.
(This one is more my opinion) Searching through the API is more intuitive than using the SphinxSE SQL syntax.