I've seen these two far, but I can't find anything on what the difference is or why one is supposed to be harder to capture than the other. Can anyone tell me?

The color of the stars just indicates their rarity which is connected to how many trait points they have. I think all the pets are all equally difficult to catch aside from needing different nets at higher rarities.

You'll first find standard snare traps at Saerielle for catching rare quality pets (blue stars). When you reach Ethernia, you can buy all the non-diamond shop nets there including the strong snare traps necessary for catching epics (purple stars). For legendary and mythics, you'd need to use a masterful snare trap that's bought in the diamond shop. All of the nets needed for a certain rarity can also be used on less rare pets, too. Like I don't bother carrying lesser snare traps usually. I mostly just carry around standards and strongs along with a few masterfuls for just in case. But because masterful traps are very expensive, I'm very cautious what I use them on.

The number of stars indicates how hard they are to battle. They can have a difference with how much mana they have as a stat after being caught though.

Clarifying a bit further:
Colour of stars indicates the number of trait points
White = common = 0
Green = uncommon = 1 (1 carry)
Blue = rare = 2 (2 carry or 1 visible)
Purple = epic = 4 (4 carry, or 2 c/1vis, or 2vis)
Yellow = legendary = 6 (6 c, or 1v/4c, or 2v/2c, or 3v)
Red = mystical = 8 (2v/4c, or 3v/2c, or 4v)

Number of stars (in non-fabled pets)
1 = 60 mana
2 = 80 mana
3 = 100 mana
4 = 120 mana
5 = Boss/Uncatchable (but 120 is the cap so it'd be 120)

Fabled pets have +20 base mana compared to the common pets of equivalent stars (capping at 3 = 120).

Thanks for the info!