Diffrence in result from PostgreSQL (PostGIS) and SQL Server (Spatial)
A couple of things that have caught you out here.

In the SQL Server version using the Point, the order of the coordinate is Lat Lon, eg Y X.  The OGC Point construct is X Y or Lon Lat.

The next is that the PostGIS query you've posted actually returns 8.20039023523232e-005 which while appearing similar to the SQL Server result, is quite a lot smaller.

The last issue is that the PostGIS query is treating the objects as Geometries and doing a cartesian distance on them.  You need to explicitly make them Geographies.

Here's a few ways to do the PostGIS query.  I've swapped the coordinate order

SELECT ST_Distance(ST_GeomFromText('POINT(88.124582 27.185425)',4326)::geography,
                   ST_GeomFromText('POINT(88.124500 27.1854258)',4326)::geography);

SELECT ST_Distance(ST_GeogFromText('SRID=4326;POINT(88.124582 27.185425)'),
                   ST_GeogFromText('SRID=4326;POINT(88.124500 27.1854258)'));

-- Adapted from the PostGIS Manual
SELECT ST_Distance(gg1, gg2) As spheroid_dist, ST_Distance(gg1, gg2, false) As sphere_dist 
FROM (SELECT
    ST_GeogFromText('SRID=4326;POINT(88.124582 27.185425)') As gg1,
    ST_GeogFromText('SRID=4326;POINT(88.124500 27.1854258)') As gg2
    ) As foo  ;