A human's method of teaching differs from most in the animal kingdom as it was copied of the Prussians who were using it to brainwash students to go into the army so the school system has little evidence backing it up and better methods have been found that are proven to work better for example
The canine method of letting the children explore and find out what happens when I do this, with the adult supervising to ensure survival this makes the learning experience fun and allows the child to realize that if the parent stops them that is dangerous and they will remember and tell their children. They fit all 3 categories.
Octopuses and Squids don't have a teaching method they are just naturally smart and self taught as most babies are left to live on their own, but it has been shown that self teaching works very well in humans as well. their brain structure is too different to compare because their brains are all throughout their body and their limbs make decisions for themselves. They fit 2/3 categories because they don't teach each other as they have no language
Dolphins teach their children through example due to this being at an early age it is fully implemented into their brains the mothers may teach them tool use or language for them to be taught later on about the social structure and hunting formations. They fit all 3 categories
Ants are extremely different from us as they are an eusocial genus they don't care for young to make sure their genes persevere instead they care for young to make sure the hive continues to exist, and their is biological differences between ants that mate and ants that don't. They think logically for the betterment of the hive, for example when it floods they remove the larvae first as they are the next generation, ants teach other ants how to get from A to B and how to distinguish A from B it is very simple but makes sense as they mainly follow instinct and pheromone trails left by other ants. They fit all 3 categories
There are many others but these seemed to be the ones being talked about here.