I've noticed that wild pets are always labeled as common, uncommon,or rare. What's the difference between common, uncommon and rare wild pets? Are rare pets worth trying to catch?

The differences between these are their genetic points, which will determine how much traits they'll have.

Common pets have 0 gp
Uncommon pets have 1gp
Rare pets have 2gp
Epic pets have 4gp
Legendary pets have 6gp
Mythical pets have 8gp

So each carried trait is 1gp, visible traits are 2gp.

Ok, so given this information, I have a question. I caught a rare pet with one visible mutation. When I sample cross bread him with another visibly mutated pet, I found that the offspring will have a collared neck (a mutation not visible in either parent). How did this happen?

Collared neck is probably a hidden trait.

A visible trait can be Homozygous: e.g. AA or Heterozygous: e.g. AB. In a homozygous visible, the trait shown will be the one designated with A, in a heterozygous AB, the trait A will be shown, but the trait B will be hidden. When an AB mates with an AB, there is a 25% chance that the offspring will be BB.

So as an example.

Let's say zolnixi G1

Visible AA is banded stripes only
visible AB shows banded stripes with hidden tribal stripes
When an AB mates with an AB, there is a chance the offspring will be
AA, AB or BB
The chance is:

25% AA - visible banded stripes
25% BB - visible tribal stripes
50% AB - visible banded (hidden tribal)

Very interesting. On e of the things I love about this game is how detailed and scientific the breeding system is. But I guess my question is, if rare pets can have only one recessive trait, then how come my rare pet has both lop ears and the ability to bread an offspring with a collared neck? Doesn't this mean that my pet has two rare traits, one dominant and one recessive?

Doesn't that mean that my rare pet has 3gp and not 2?
His name is Leo, if you want to look at him.

Doesn't that mean that my rare pet has 3gp and not 2?

No. If the sylesti you caught was a rare (a blue star) then it will have 2gp regardless if it has a hidden trait in its vis or not.

1gp is for 1 letter, which is always a carried trait. So for example; this lovely boy of mine is a 1gp - therefore, a 1 carried

https://www.sylestia.com/view/pets/?petid=1524527

Genetically he shows up as G2: (NA) Where N signifies nothing and A signifies Frosted Tips (by the way, the letter N is not counted as a GP letter. It's a void symbol: N marks something that does not actually exist.)

2gp is for 2 letters. These two letters can signify either a 2 carry, 1 homozygous, or 1 heterozygous

a 2 carry, e.g.

https://www.sylestia.com/view/pets/?petid=1713085

This boy shows up as G1(NI) and G3 (NA)

1 homozygous vis, e.g.

https://www.sylestia.com/view/pets/?petid=1927882

This girl is visible for Ladybug Wings only. She is M1 (FF)

1 heterozygous vis. e.g.

https://www.sylestia.com/view/pets/?petid=2042678

This girl shows up as M1 (BG) She is visible for Gem Wings and is hidden for Mantis Wings. She is still a 2gp because there are only 2 letters in her genetics. (If you look at this one in the advanced search, you can see it more clearly: her dominant trait and letter, and her hidden one).

- Finally, in order to verify if a pet has any hiddens or carries, you will need to genetically test the pet. I and many other people offer free testing services.

"if rare pets can have only one recessive trait, then how come my rare pet has both lop ears and the ability to bread an offspring with a collared neck?"

Loppy ears is signified by (F) - Although I can't see any trait called collared neck. Are you speaking of Tassel Costume trait (C)?

If this is the case, then tassel costume is dominant to lop ears (lower letters are dominant - higher letters recessive). If you Mate an F mutation with a C, then the offspring will be CF, showing tassel costume, with hidden ears. But this depends on the partner of the sylesti in question.

It's quite possible then that Leo is homozygous (FF), if his partner is either carried or vis for (C) - but I can't really tell unless you were to get him tested!

Hope this helps! Sorry if it's a bit convoluted.