there is a question. If you add Sphinx search to a PHP program, such as a website made by laravel, do you use SphinxQL or SphinxAPI?

Applications can access Sphinx search daemon (searchd) using any of the three different access methods: a) via Sphinx own implementation of MySQL network protocol (using a small SQL subset called SphinxQL, this is recommended way), b) via native search API (SphinxAPI) or c) via MySQL server with a pluggable storage engine (SphinxSE). 

official statement using a small SQL subset called SphinxQL, this is recommended way
all the materials you can find now are SphinxAPI to combine PHP, whether there are examples of SphinxQL + PHP combination.