I’ve taken a look at Futato’s article and his arguments for the meaning of these two categories of vegetation seem valid (though I haven’t done serious study of the terminology myself).
I would, however, qualify the absolute sounding statement he makes that “The word, s´îah, occurs only four times (Gen 2:5, 21:15; Job 30:4, 7).”
He is correct that the noun s´îah (meaning bush) occurs in only four places in the OT and suggests (from the context) naturally growing vegetation in the wilderness rather than cultivated plants.
But s´îah has another (more common) meaning in the OT, namely to muse, complain, meditate (a verb) and a meditation or complaint (a noun). So his statement needs nuancing.
As for what hassadeh means, it is literally “the field.” When attached to hayyah (living creature or animal) in Genesis 2-3 it means wild animal (field works here the way we distinguish field mouse from city mouse in the fable). So it would be logical to see s´îah hassadeh as a wild bush/plant.