Which pets are NOT account wide?

[Klehley]

Is there a list somewhere? I have 151 on my Paladin and only 149 on my new Monk...What gives?

[Plucky]

Is the monk....a Pandaren?

If so, you'll probably have to progress far enough on the starter island to pick a Faction, unless the pet's you're speaking of happened to be something like Argent Tourney Pets or something weird?

[Spyro]

As far as I know:

Moonkin Hatchlings: Both versions will show in your list but you can only summon the one for your faction
Horde/Alliance Ballons: Both versions will show in your list but you can only summon the one for your faction
Argent Gruntling, Argent Squire: Both will show in your list if you have obtained both but you can only summon the one for your faction
Guild Heralds and Guild Pages: These seem to be the only pets bound to individual characters.

[Breanni]

As far as I know:

Moonkin Hatchlings: Both versions will show in your list but you can only summon the one for your faction
Horde/Alliance Ballons: Both versions will show in your list but you can only summon the one for your faction
Argent Gruntling, Argent Squire: Both will show in your list if you have obtained both but you can only summon the one for your faction
Guild Heralds and Guild Pages: These seem to be the only pets bound to individual characters.

This is exactly correct. And add the Alliance and Horde balloons to the list of pets where both show, but only your character's faction's balloon can be summoned.

So really just the Guild Heralds and Guild Pages are truly limited to one character.