You are probably looking for Functions for Testing Spatial Relations Between Geometric Objects
The functions described in these sections take two geometries as input parameters and return a qualitative or quantitative relation between them.
From the manual:
Note MySQL originally implemented these functions such that they used object bounding rectangles and returned the same result as the corresponding MBR-based functions. As of MySQL 5.6.1, corresponding versions are available that use precise object shapes. These versions are named with an ST_ prefix. For example, Contains() uses object bounding rectangles, whereas ST_Contains() uses object shapes.
As of MySQL 5.6.1, there are also ST_ aliases for existing spatial functions that were already exact. For example, ST_IsEmpty() is an alias for IsEmpty()