I just captured this aurleon after I saw it was epic while battling it. https://www.sylestia.com/view/pets/?petid=7194647

But... it only has one trait? Rares have one trait as well. This guy (https://www.sylestia.com/view/pets/?petid=7146611), for example, was a rare while battling yet seems to be identical to the epic with just different traits.

I know commons and uncommons have no traits, but what's the difference between rare and epic if they both only have one trait?

Only commons have no traits, not uncommons.
The issue you're having is that if a pet isn't genetically scanned/gene tested, you cannot see Carried traits (or hiddens under vis traits). They can still pass the trait(s) on to offspring, you just can't see the trait in the pet in question's info.

There are plenty of people who offer gene testing for free in the clubs/guilds/services forum.

Unfortunately the only way to really get a gene test kit or genetic scanner these days* is the newbie kit one-use ones, sometimes during advent (non-tradable, sadly), and the infinite-use ones from the diamond shop (hence how people can offer free testing). Those are very good to get, if you can get the diamonds (either buying them directly or using currency exchange to buy enough diamonds from other players)
(* used to be that they were a common consolation prize from fest wheels, but those were retired years ago now)

You can see if a pet has been genetested by if it has a little test kit icon in its info.

Rarities are as follows:

Common, White star
No trait points

Uncommon, green
one trait point (1 carry)

Rare, blue,
two tp (1 vis trait, or 2 carries)

Epic, purple
four tp (2 vis, or 1v2c, or 4c)

Legendary, yellow
six tp (3v, or 2v2c, or 1v4c, or 6c)

Mythical, red
eight tp (4v, or 3v2c, or 2v4c)

Oh, thank you! That makes a lot of sense! I'll see if I can save up for an infinite use test kit sometime in the future (it is a bit expensive for the moment).
I didn't know carried genes could occur in tamed sylestis, I thought they were just a generator thing.

Is there a guide i keep seeing three blue star star slyestia that seem not that impressive

all blue and purple star non-themed sylesti+ blue star themed in the lost grove have three stars, it's just an indicator of their strength (lg stats-wise).
We have a guide page here

Thank you so much ,.I've saved the guide dor safe keeping