Postgres has similar SQL commands.

Commands that start with \ are shortcuts in the psql client that are translated into SQL commands.

You can always use SELECT * FROM pg_tables; and operate on those tables as if it was a normal SQL relation (because it is).

Additionally, if you use psql -E, it shows you the SQL it runs for such shortcuts. For \d (Show relations) it runs:

    SELECT n.nspname as "Schema",
      c.relname as "Name",
      CASE c.relkind WHEN 'r' THEN 'table' WHEN 'v' THEN 'view' WHEN 'm' THEN 'materialized view' WHEN 'i' THEN 'index' WHEN 'S' THEN 'sequence' WHEN 's' THEN 'special' WHEN 'f' THEN 'foreign table' END as "Type",
      pg_catalog.pg_get_userbyid(c.relowner) as "Owner"
    FROM pg_catalog.pg_class c
         LEFT JOIN pg_catalog.pg_namespace n ON n.oid = c.relnamespace
    WHERE c.relkind IN ('r','v','m','S','f','')
          AND n.nspname <> 'pg_catalog'
          AND n.nspname <> 'information_schema'
          AND n.nspname !~ '^pg_toast'
      AND pg_catalog.pg_table_is_visible(c.oid)
    ORDER BY 1,2;