I've seen people selling mythical and legendary pets, but when I click on the profile of a pet it seems no different to me than any other pet. What does it mean that a pet is mythical or legendary?

Legendary and mythical pets are a type of rarity. They have yellow and red stars respectively when you encounter them in the wild. A legendary pet has yellow/orange stars and has a base GP/TP of 6. (6 carried traits, 2 vis/2 carry, 1 vis/4 carry or 3 visible before mutation) Mythical, or red stars, have 8GP/TP.
Legendaries can also be found in the wild as eggs or even bought from the scale shop for 1900+ scales (no fabled or Kelpari/Lunemara) and legendary/mythical Puffadore and Ny'vene can be purchased from their shops for a massive amount of marks/badges.

I have stables filled with legendary pets if you want to look at them and get an idea.

and beyond those things that Imperium listed, they're pretty much the same as regular pets, with the excpetion of if the pet is caught in The Lost Grove, wherein wild higher rarity pets get much higher bonus stats.

For wild (non-eggling, non-themed) pets:
Common : +0
Uncommon : ~+6
Rare : ~+10
Epic : +20-30
Legendary : +30-45
Mythical : +30-45

(unthemed Egglings will have the equivelant to Rare pets, Themed Egglings match Epic, and Themed Wilds have a different set of stat brackets that are higher than unthemed wilds of equivalent rarity)

Thank you both. Are higher rarity pets worth more if you are selling them?

They're certainly worth a lot more then common, uncommon, rare and epic. They usually also require master snare traps though if you're catching them. (Once again, with the exception of the Lost Grove, but that's a painful route.)