Is “a special melee attack” an actual game term?

PHB page 195 mentions "special melee attack" when talking about Grapple and Shove:

you can make a special melee attack to shove a creature

you can use the Attack action to make a special melee attack, a grapple

It uses words "make a special melee attack" like it is a thing in 5e, however, nowhere in the game text it’s being said what a "special melee attack" actually is. It isn’t even mentioned anymore. I believe that "special attack" is not a game term — it’s a vestige from the previous editions, where "special attacks" was a thing, but I could be mistaken.

Are there any other examples of "special melee attack" (or just "special attack") in any official source book for 5e?

I was searching through dndbeyond and the only thing I’ve found was Sword Of Answering. But it uses words "special attack" in the context of the magic item description:

while you hold the sword, you can use your reaction to make one melee attack

any damage dealt with this special attack ignores any damage immunity or resistance the target has

You can remove the word "special" from its description and nothing changes. So it is plain English meaning here, not the game term.

So what is a "special attack" in terms of the game mechanics?