Yes

One example is Ring of the Ram which can be used to "attack" a creature within 60ft. Although this is an attack at a distance, it is not listed as ranged, nor as melee.

No

All attacks are melee or ranged. They might additionally be spell attacks, weapon attacks, improvised attacks, or something else, but they're always melee or ranged.

The reason for calling out both is not to imply a third category, but to specify that all attacks are forbidden. Sometimes "attack" tends to read as "melee attack" or "weapon attack", so calling out both ranged and melee is just meant to make it more clear that it's affecting everything. (For example, slow would prevent you from using scorching ray to its full effect, because while you would theoretically get three or more rays to fire, you can only roll one ranged spell attack due to the slow effect.)

In one of Jeremy Crawford's appearances on Dragon+, he commented that there are several examples of confusing "reminder text" in the Player's Handbook that they regret in retrospect for exactly this reason. They added what were meant as reminders of rules printed elsewhere that inadvertently feel like they imply something that wasn't intended.