Hair grass is not a true aquatic plant, neither is Anubias.
Lots of plants are sold as aquarium plants and most are marsh plants that do really well when their roots are in water and the rest of the plant is above water. Some marsh plants will do well underwater too.
Some common marsh plants include Amazon sword plants, Hygrophila sp, Rotala sp, Ludwigia sp, Bacopa sp.
True aquatic plants include Vallis, Ambulia, Cabomba, Hornwort, Elodia, Hydrilla.
The main difference between marsh plants and true aquatic plants is the stem. True aquatics have a soft flexible stem with air bubbles in it. These bubbles help the plant float and remain buoyant in the water column.
Marsh plants have a rigid stem and these plants can remain standing upright when removed from water. Whereas true aquatic plants will fall over/ collapse when removed from water.