While the underlying index should be opaque to the user of a DBMS with spatial features, the API used to define spatial types and operate on them is of course more visible. The relevant standard in this space is often referred to as "OpenGIS", however the Open Geospatial Consortium in fact defines a long list of standards. The standard relevant to SQL databases is known more precisely as "OpenGIS Implementation Specification for Geographic information - Simple feature access - Part 2: SQL option" aka "Simple feature access".
It is not meaningful to recite the standard at length in my blog, my focus is instead on actual implementations that I will blog about later. The following points are however worth noting: