Huh, that is weird. Double checking the rest of the generation if you have 1 ability you are in these categories:
-You have a signature ability and it is your Designated Gimmick (Mimikyu's Disguise, Minior's Shields Down, Beast Boost, stuff like that).
-You have Levitate (Vikavolt)
-You evolve into someone with that signature ability (Grubbin, Charjabug, Type Null, Cosmog etc)
-Mythical pokemon
....and Turtonator. Wonder if it was meant to have a signature ability to go with it that just never happened? Should have given it a proper, if still normal hidden ability in gen 8 at the very least...
Turtonator is a case of a Pokemon who was intended to have a signature
move as opposed to a signature ability. Not every Gen 7 mon has a signature ability, but the ones that don't have a signature move to go with it. Some Gen 7 Pokemon have both, but many either only have a signature move or only a signature ability.
With respect to Drampa, the two are opposites in treatment in this regard, where one only has a signature move and the other only has a signature ability. Turtonator has a signature move, Shell Trap, which is basically its gimmick to be a powerful reactive move. It does not, however, have a signature ability. Drampa, on the other hand, has a signature ability in Berserk, however, it has no signature move to go with it.
Another counterpart duo has this sort of treatment, which is Oranguru and Passimian, in which case they both have a signature move/ability that works with Doubles in mind. Oranguru does not have a signature ability, but it has a signature move in Instruct. Passimian meanwhile does not have a signature move, but it has a signature ability in its ability Receiver.
In fact, going down Gen 7's mons, these are cases of signature move/signature ability cases:
Signature Move Only:
- Incineroar (Darkest Lariat)
- Toucannon (Beak Blast)
- Crabominable (Ice Hammer)
- Ribombee (Pollen Puff)
- Lycanrock (Accelerock)
- Alolan Marowak (Shadow Bone)
- Lurantis (Solar Blade)
- Shiinotic (Strength Sap)
- Oranguru (Instruct)
- Turtonator (Shell Trap)
- Togedemaru (Zing Zap)
- Alolan Exeggutor (Dragon Hammer)
- Kommo-o (Clanging Scales)
- Marshadow (Spectral Thief)
- Zeraora (Plasma Fists)
- Melmetal (Double Iron Bash)
Signature Ability Only:
- Gumshoos (Stakeout)
- Alolan Raichu (Surge Surfer)
- Charjabug (Battery)
- Alolan Dugtrio (Tangling Hair)
- Wishiwashi (Schooling)
- Mudsdale (Stamina)
- Araquanid (Water Bubble)
- Salazzle (Corrosion)
- Bewear (Fluffy)
- Wimpod (Wimp Out)
- Alolan Muk (Power of Alchemy)
- Alolan Golem (Galvanize)
- Minior (Shields Down)
- Komala (Comatose)
- Mimikyu (Disguise)
- Drampa (Berserk)
- Ultra Beasts except Blacephalon (Beast Boost)
Both signature move and signature ability:
- Decidueye (Long Reach ability, Spirit Shackle move)
- Primarina (Liquid Voice ability, Sparkling Aria move)
- Oricorio (Dancer ability, Revelation Dance move)
- Toxapex (Merciless ability, Baneful Bunker move)
- Tsareena (Queenly Majesty ability, Trop Kick move)
- Comfey (Triage ability, Floral Healing move)
- Golisopod (Emergency Exit ability, First Impression move)
- Palossand (Water Compaction ability, Shore Up move)
- Pyukumuku (Innards Out ability, Purify move)
- Silvally (RKS System ability, Multi-Attack move)
- Bruxish (Dazzling ability, Psychic Fangs move)
- Tapus (Surges ability, Nature's Madness move)
- Solgaleo/Lunala/Necrozma
- Magearna (Soul-Heart ability, Fleur Cannon move)
- Blacephalon (Beast Boost ability, Mind Blown move)
Neither:
- Alolan Raticate
- Vikavolt
- Alolan Ninetales
- Alolan Sandslash
- Alolan Persian
As you can see there is a mix between signature moves and signature abilities: Some only have one or the other, while only some have both.
In the case of Turtonator and Drampa, they went for the two to be antithetical to each other with one having only a signature move while the other only has a signature ability.