The distinction can matter because the core purposes of the two are different. A "Labor" union is one that represents one side of the relationship between capital and the workforce: that is, the side that has a portion of the value it creates in its work extracted by the other.

It exists fundamentally in order to be able to collectively negotiate around the amount of that value extracted and attempt to retain more for those who create it. That in doing so it also establishes workers' rights, policies around treatment etc is a nice to have.

The police, as an extension of state power much like the army, are generally understood to be broadly on the "side" of capital (in capitalist states). They are not value-creating, and their "unions" have nothing to negotiate for a share of. This is why you'll more often see them represented as "associations" or "federations", much like civil service, nursing or fire service staff bodies. Their goal is simply to argue for better terms and conditions for their members.

Does the distinction practically matter? In many cases, no. When the interests of capital or the state are at stake, yes: police officers will break up labor union strikes, even when those officers are members of a federation. They are fundamentally not part of the same movement.