Those two pets are in different families! The Stone Dragon Turtle is part of the Turtle family. Myonix is part of the Spirit Beast family.
They’re both Tenacity spec. This means the two spec abilities they get are “Endurance Training” (passive 5% health buff) and “Survival of the Fittest” (active reduced damage for 6 seconds).
The turtle gets the Turtle Family specific ability “Shell Shield.” This is an active ability which you can either leave automatic or toggle yourself. This reduces the damage the turtle takes by 50% for 12 seconds.
The spirit beast Myonix gets 3 abilities because it’s an “exotic pet family” (meaning only BM hunters can tame them). Exotic pet families gets extra abilities. So Myonix has: “Spirit Shock,” which removes 1 enrage/1 magic effect from the target, “Spirit Walk,” which puts your pet into stealth and gives a 20% bonus to the first attack, and “Spirit Mend,” which is a heal that you could put on any friendly target.
“Spirit Mend” is the reason so many BM hunters run with Spirit Beasts in mythics and raids, to help out with healing.
Turtles are a little tricky to use, because their pet ability (Shell Shield) has to be carefully timed. If you use it at the wrong moment, it turns into a penalty instead of an assist. That’s why some hunters prefer to run with pets which has passive shielding abilities (like a bear or a clefthoof).
Also, like I mentioned before, due to the way stats work, Ferocity pets actually are better tanks than Tenacity pets. It’s because the Ferocity pets have passive self-healing due to the 10% Leech bonus. Tenacity pets don’t have that, which means they require a LOT more active healing.
Please feel free to experiment with pets! You have 55 stable slots, and can carry 5 pets around with you. That gives you 60 options.
I do highly recommend trying a Ferocity pet. If you want an exotic Ferocity pet (which means they come with 2 to 3 extra abilities), you can try a: Chimera, Clefthoof, Core Hound, or Devilsaur.
These are Ferocity pets, which means they come with the 10% Leech buff and the Bloodlust (“Primal Rage”) active buff. Being exotic, those 4 families come with 2 extra pet abilities.
If you’re fine with trying the non-exotic Ferocity pets, they are: Bat, Carrion Bird (like vultures), Cat, Crocolisk, Gorilla, Ravager, Ray (like mana rays), Scalehide, Scorpid, Spider, Tallstrider, Wasp, Wind Serpent, and Wolf.
So far, it seems like you’ve tried mostly Tenacity pets (turtles and spirit beasts). Don’t be shy to try out the other specs!
Just so you have all the information, Cunning pets provide: “Pathfinding” passive buff (a 8% movement bonus) and “Master’s Call” (pet removes impairing effects from target. AKA pet frees you from a trap. This is a PvP ability).