In the Druid bond ability for animal companion, it states that the companion can grow in size at levels four and seven. Is this universal to all animal companions in Pathfinder (say, a Ranger's companion or the new Hunter class in the Advanced Classes playtest) or is it specific only to the Druid?
And a second question based on a answer of no, only the druid, is there a way to get a permanent size increase to a companion?
Specific companions like the wolf get bigger at specific levels listed in that specific choice. Anyone who gets an animal companion has it advance at an effective druid level and it will increase in size at the listed time.
Classes like ranger have an 'effective druid level'. For rangers, their effective druid level is their ranger level -3. Other than that, it works exactly the same. So if an animal would grow in size at 4th level, it would do so at level 7 for a ranger.
There are various feats though that increase effective druid level. Boon companion is the most common, giving you +4 to the EDL, up to your character level's worth.
EDIT: noticed from the diction- do you think they all go through two size increases? No, levels 4 and 7 just the points where a size increase would happen, if it does happen. A wolf, for instance, grows to large at effective druid level 7. Until then, it is just medium. A small cat (leopards, cheetahs), however, have their size increase at level 4. And horses never go through a size increase. But even if there is not a size increase, there is usually an increase in stats and such at one of those two benchmarks.
Just read the stat blocks on :this link, and you will start to get the general picture of how animal companions advance.