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PostGIS offers a list of operators implementing spatial relations. Some of them have a direct function equivalent, for example <-> and ST_Distance.
EXPLAIN
SELECT
st_distance(st_setsrid(st_makepoint(0, 0), 4326),
st_setsrid(st_makepoint(10, 10), 4326))
and
EXPLAIN
SELECT
st_setsrid(st_makepoint (0, 0), 4326) <->
st_setsrid(st_makepoint (10, 10), 4326)
yield the exact same query plan. Are there any scenarios in which one method is preferable to the other?
<-> and <#> can make use of indexes when used in SORT BY clause.
Used in the "ORDER BY" clause provides index-assisted nearest-neighbor result sets.
e.g.:
SELECT *
FROM table1, table2
SORT BY table1.geom <-> table2.geom
LIMIT 1
See the example on the docs for <->.
Another difference:
<-> always uses spherical distance for geography type, while st_distance uses distance calculated on a spheroid (slower) as default with an option to change it (use_spheroid=false).
For PostgreSQL below 9.5 only gives centroid distance of bounding boxes and for PostgreSQL 9.5+, does true KNN distance search giving true distance between geometries, and distance sphere for geographies.