Apart from the druid that uses the standard rules for animals companions, most other classes that grant an animal companion of some kind give a few special benefits and drawbacks. Examples with two classes that interest me : the cavalier and the mammoth rider :
The cavalier has a very limited choice of bonded mounts : camel or horse for a Medium PC, pony or wolf for a Small PC. A cavalier can get only one bonded mount, it's always combat-trained and has Light Armor Proficiency as a bonus feat, and the cavalier can replace a dead mount only after one week of mourning, and the new one doesn't get all animal companion special abilities until the cavalier levels up.
The mammoth rider gains one steed among a small list of animal companions that are typically Large at level 7 (this class requires a level 6 animal companion to qualify), except the steed becomes Huge, gaining the standard benefits and drawbacks of this new size as well as ability score adjustments and a natural armor bonus that keep progressing with mammoth rider levels.
If a halfling cavalier who chooses a wolf as a mount wants to become a mammoth rider, does the current bonded mount (the wolf is in the list of mammoth rider steeds) get every special benefit and drawback from both classes ? Or does the mammoth rider steed rules override some of the cavalier bomded mount rules ?