For Postgres, efficiently get points within X distance of point Y?
I only need the distance to be accurate on a local scale and so curvature of the earth shouldn't be an issue for my application, but is there a performance benefit of either POINT or GIS in this context?


The native point is for geometry. If you want distance on Earth then those "points" are being projected onto a representation of Earth (sphereoid) and you need GIS. If you're using PostgreSQL that means you need PostGIS. For a PostGIS query that returns all points in a table within a 1 km (1000 m) distance of a specific point, you can use ST_DWithin

SELECT *
FROM tbl
WHERE ST_DWithin( tbl.geog, ST_MakePoint(x,y)::geography, 1000 );


That will also use a GIST index (if any) on tbl.geog.