Yes. But to elaborate, there are 10 possible breeds (not considering gender, which doesn't impact stats). A pet has 'base stats', e.g. 8/8/8 or 7/9/8, which add up to 24 within some limits. Then the pet gets between 1.5 and 2 'bonus' points, which is determined by the breedID. 2 bonus points in power is breedID 4, etc. There is a very good explanation and list of breeds here
Now, as far as 'health = tank', I would argue that the best stats for a pet depend on its moveset. For a tank such as a crab or spider, power trumps health, because heals and shields benefit from power and not health. Magical Crawdad on the other hand benefits most from health, but this is a special case because his Wish ability is so strong and is based on health instead of power.
For example, Molten Hatchling (who I'm guessing you're partial to, from your avatar) is an excellent tank despite having rather low health (1319 at a maximum). This is due to having 2 heals that both have high coefficients, and relatively high power (276-305). Molten Hatchling doesn't exist as a breedID 6, so it wouldn't come up your search for tanking pets. And, if it did, I'd still want one with higher power instead.