Hello Mandy! rarity has to do with the traits a pet has.

1 GP = one carried trait
2 GP = two carried traits OR one visable trait

So the following applies to tamed sylesties and can be used to tell you how many GP a pet has

common- no color= no GP. This pet posseses no traits at all.
Uncommon- Green= 1 GP. This pet carries one gene
Rare- Blue=2 GP. This pet carries 2 traits OR shows one visible trait.
Epic-Purple= 4GP. This pet carries 4 traits, OR this pet has 2 visable traits OR this pet carries 2 traits and shows one visible trait.
Legendary-Orange=6gp. This pet carries 6 traits, OR this pet shows 3 traits, OR has a combitiantion of carried/ vis equalling 6 total GP.
Mythical-Red=8GP. This pet shows 4 traits OR has a combination of carried and visable traits totalling up to 8 GP.

You will notice that the color of the trap also corresponds to the highest GP the trap is able to catch. So for example, you can use a green trap to catch an uncommon or common pet, but not a rare, epic, legendary, or mythical pet.

Orange and Red star pets (legendary and Mythical) can only be caught with a masterful snare.

Common means no traits at all.
Uncommon and rare have different meanings depending on if you are in Viridian Meadows and Umbra Forest or Astryls Vale.
In the first two regions: uncommon=1 visible trait and rare=1 visible trait and 1 carried
In the third: uncommon=1 carried trait and rare=1 visible trait or 2 carried traits

So if you got this pet from either Sweet Blossom Orchards or Astryls Tranquility, it is very likely that it is a 2-carry and you would need to get it tested to see the carries.

Thank you both very much !!
Helped me out a lot ! ^-^