Furthermore, we've always ruled (this had actually some support in previous editions, and it does in 5th too as far as characteristics are involved) that the markings of the form mirror those of the human: an old, one-armed, fat human becomes an old, three-legged, fat wolf.
Inner Heartshape ignores various flaws. So does Ettin-mod.
Tytalus and Infernal virtues allow variant forms within a species.
Distinct spells (or whatever they are called in a given tradition) allow changing size.
Virtues and Flaws that affect size do not carry over; virtues and flaws that affect characteristic indirectly carry over; none of this alters the 1:1 correspondence of shapes.
A daimon (the real one that is hidden away) can have manifestations with different attributes and perhaps even shapes, depending on the spell used to summon it. There is still a 1:1 correspondence, of a kind.
It is probably reasonable for a magus to invent a MuCo(An) that allows a Finesse roll to alter the appearance of the animal, as long as the change is cosmetic (ie, does not grant a missing limb, does not give the animal any bonus other than for being disguised as a particular animal, etc). +1 magnitude seems reasonable. Creo would be needed to, say, restore a limb for the duration...
Actually, Size does not carry over. Virtues and Flaws that affect Size do. This way you don't get a double-counting by accident. Here's why:
Without such a rule, you might have someone with Small Frame turn into a bear. -1 to Size carries over, so the bear goes from +2 to +1. Flaws carry over, so this bear gets Small Frame, lowering its Size by 1. The bear goes from Size +1 to Size 0. Small Frame has reduced the bear's Size by a net of 2.
Oops. So we avoid this by keeping Virtues carrying over but not carrying over Size. However, they never wrote in the equivalent corrective part for Characteristics. So, technically, you could take Improved Characteristics, have them increase your human Characteristics, adjust the animal Characteristics accordingly (theoretically improving them), then carry over the Virtue Improved Characteristics and use it to raise the animal Characteristics further. Clearly this is a flaw inherent to the rules. There are a few issues with the animal rules that could have been avoided with some small changes, nearly keeping things as-is. Oh, well, at least they're generally reasonable.
What I mean is that, iirc, when a person with Small Frame becomes a bear, the bear's size remains +2. So the v/fs affecting Size do not carry over.
If I remember wrong, that's a different matter.
I might be missing an important case, but for all attributes other than Int, I'd want to just add the human and animal attributes. So a strong but clumsy human becomes an even stronger but even clumsier bear.
In general, the shapechanging rules work poorly when changing from one non-human to another, because of the post-core-rules change that causes Size to modify Characteristics. To get sensible results, first Size must be undone for the creature, and then the shape change rules (which includes size so interesting things happen.) It would have been better for Size to leave the attributes untouched but provide bonuses (2*Size bonus for Str, etc.)
In a deeper sense, if all changes to a species' normal Characteristics and abilities etc were represented by virtues and flaws, then changing shape would involve taking the new baseline and applying your extra v/fs. So an average bear transformed into a pigeon becomes an average pigeon; a strong, large but Infamous bear with Premonitions becomes a strong, large but Infamous pigeon with Premonitions; etc. With this method, Size being attached to characteristics no longer matters, since Size is either part of the species package or part of the individual's v/fs.
I'm not sure the 8 characteristics we have are the most appropriate set, but that's a different conversation. (One can justify these 8, but that's not the same as this set of 8 helping the game more than a different 8, or a set of 13, 4 or 0.)