Only true aquatic plants or marsh/bog plants that are naturally "programmed" to live submerged partially or totally are suitable in aquaria. Among the latter I am thinking of swords (Echinodorus species), crypts (Cryptocoryne species), Anubias
, etc., that in their habitats usually (though not always) live half the year emersed (when they all flower) and half submersed (the rainy or flood season). They adapt to fully-submersed cultivation (as in the aquarium) very well. These mostly produce different types of leaves when grown submersed from emersed, and this is the reason most terrestrial plants will not last submersed.
The structure of the leaf is vastly different; terrestrial plants have heavier, thicker leaves because they must conserve water while allowing respiration (exchange of gases). Aquatic plants have much thinner leaves that generally do not stand up out of water because they lack the strength of structure; their purpose is to allow free assimilation of nutrients from the surrounding water, as well as the exchange of gasses (oxygen/CO2) via water. Their cell structure is quite different.
Most true terrestrial plants will, if attempts are made to grow them submersed, rot completely within a fairly short period.