ST_Overlaps() – only polygons selected where their boundaries touch the box boundary and any part of the polygon area is inside the box.

ST_Intersects() – all polygons selected where any part of the polygon (boundary and inside) are in or touch any part of the box, though it seems to have missed some from the upper-right neighboring cells.

ST_CoveredBy() – only polygons where the boundary and area are completely inside only the area of the box and not touching the box boundary.

ST_Within() – similar to st_coveredby, except that it only seems to look at the outer boundary of the polygons, and that upper-right corner polygon is actually an invalid polygon where the "outer" polygon is "hole" polygon (not visible here), thus inside and not touching the box boundary.