This plant grows in muddy areas along lake edges in small colonies.
Sometimes the name Frogfruit is used instead of Fogfruit. An internet search for Frogfruit yields 125,000 results and Fogfruit gives 10,900 results. So, via scientific analysis, Frogfruit is prefered 10:1 over Fogfruit.
So, why two names. Well, the first name given was Fogfruit. Fog is an old Scottish word for moss, referring to the growth habit of the plant. The second name of “Frog fruit” first appeared in 1834 in “Botanical Teacher for North America”. This second name appears to be a typo, since it is also referred to as “Fog-fruit” in the same book.
The name “frog-fruit” is then used in another publication in 1852 – “Catalogue of Flowering Plants and Ferns: Observed in the Vicinity of Cincinnati”.
And thus a new name was born.
Obviously people prefer the name of Frogfruit over Fogfruit, either for alliterative value or because the image of a frog is easier to remember than the old Scottish name for moss. Call it what you will.