Is “Shove” an attack?


This question is prompted by reading this answer to a question about using the Polearm Master feat’s bonus action after a Shove and halbard Attack

In the section “Making an Attack” (PHB, page 194):

If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.

Shoving does not require an attack role but rather a contested Athletics check.

Under “Shoving a Creature” (PHB, 195)

Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. […] You make a Strength (Athletics) check contested by the target’s Strength (Athletics) or Dexterity (Acrobatics)check (the target chooses the ability to use).

The text specifically says Shove is a “special melee attack”
Is this a case of “specific beats general” where the specific wording of Shove makes it an attack even though the general definition of an attack is different? Alternatively is the wording of shove just using common language or is it intended to mean something different?