I dont' think it's the "stiff" type of hornwort (there are two types of hornwart available commercially).
Info that I got from google...
The 2 types are:
Ceratophyllum demersum (more common) and Ceratophyllum submersum
Ceratophyllum demersum - common or rigid hornwort
Leaves once or twice-forked
Darker green, but new growth at high temperatures can be a pinky-green. Colour is variable in both species.
Denser
Shorter leaves
Fruits with 3 long 'spines'
Often with pink stems
The plants stems tend to float just below the surface of the water and can reach over a metre in length in the aquarium. Whilst growing best under good light it does not seem to cut out much light to plants below it, these seem to grow as normal. It will survive quite low light levels but growth is very slow or non existent. It is slower growing a lower temperatures and will form thicker leaves which give it the appearance of a different species. Either can be used as it will adapt to the temperature provided. In ponds it forms thick buds in the Autum that sink to the bottom which give the impression that it has been killed by the frost but come spring these will grow back into the long stems slowly filling up the pond. It grows continually in the tropical aquarium and if conditions are to its likening can form dense forests into which fry may escape, penetration being slow or denied to adult fish. Whilst light clumps will provide a refuge for harassed adults. Fairly tough but long stems will snap if roughly handled. Propagation is by division and is easy as even the smallest piece of stem will eventually grow into a new plant. It excretes substances toxic to algae (allelopathic behaviour) and at good growth conditions it efficiently inhibits most algae growth.
Ceratophyllum submersum - spineless hornwort
Leaves thrice-forked
Longer leaves.
Fruits have one or no spines.
Lighter green
Both are cosmopolitan in their range, so there are lots of alternative common names. So if you are doing, for instance, a Google search, use the Latin name and not the common name!
Since both occur over a wide range, both are very variable in their appearance, depending on temperature, light level and also on water hardness. The two seem to be quite similar, but most of the following refers specifically to Ceratophyllum demersum.
It is said that the spineless variety (Ceratophyllum submersum) is a prettier aquarium plant, being bushier with longer 'leaves'. That may be true, but the common hornwort's tropical form is a beautiful aquarium plant, being much more colourful than the spineless one, as the photograph of Ceratophyllum demersum shows.