The rarity is not the same as the silver dragon rare mobs found around the place a every day Rabbit or Squirrel or Bettle can be rare, when it comes to battle pets it's not the limit of that type that makes it rare (like it is with the silver dragon rare mobs) but the 'Quality' of battle stats it has.
Each battle pet has stats for it's level, some are blessed with awesome stats while most will have the standard or sub-standard stats. For example a lvl1 Hare might have the stat rating of poor (grey) common (white) uncommon (green) or rare (blue), it still looks the same as any other hare but a rare hare will have better stats (HP etc) then a poor one for it's level. The beauty is you don't know if it's uncommon or rare until you capture it so you might fight a baby bear and think it's awesome because it's always sleeping and regaining health but when you capture it it could just be a poor rated bear.
After battling so many bugs, hares, toads etc etc of the same level it's fairly easy to pick which one has better stats, but this often results in a uncommon find (well for me it does.) I've recently found a rare lvl6 snail and I knew it was special because all other lvl6 snails I had faced before it had around 450-550HP but this one had a 600HP rating, it also hit harder and lasted longer so when it was low enough in health to capture I captured it and lo-and-behold my first rare (I've caught some uncommon ones up until then.) This snail was the 9th I battled in the one area. Also the spot doesn't mark it rare, I logged onto a different realm, flew to the same spot and after battling snails for over an hour not one produced a rare snail for me... so I also think it's RNG on the stats.
My second rare was a pet that joined a battle (in some fights other battle pets team up with the pet you've challenged) it was a Forest Moth and just kept firing it's balls at me while silked so after burning through two of my pets my last one got it down to enough health to capture. Again went back to the same area on other toons on a different realm and nothing, only poor graded moths.
So yeah a rare battle pet is not the same as a rare silver dragon mob. It's to do with the stats it has. Nothing visual marks it as rare, only when you battle it does some of it's specialness shine through.Also you can scroll over the second and third battle pets that join a fight and look at their stats as well which helps in the decision if you want to capture one or not.
For those of you who haven't paid attention to your pets up until now and you want to know what your pet is rated at open your pet book (Shift+P) and click on the pets you've captured, under it's HP, Power & Speed there is a tiny dice and next to that dice will list either Poor or Common or Uncommon or Rare (this rating will show up only on the captured pets, not the drops or TCG etc etc, only those wild ones you capture in battle.) If you don't want a book full of poor quality pets (or multiples) just right click on the icon of the unwanted pet and select release and it deletes the pet from your book permanently.
Having said all this there are uncommon skins - like Minfernal, Baby Ape, Arctic Fox Kit, Qiraji Guardling, Restless Shadeling, Silithid Hatchling, Stone Armadillo, Tiny Bog Beast, Wanderer's Festival Hatchling etc etc however netting one of these doesn't guarantee a rare, again it's to do with the stats. You could wait days for a minfernal to spawn but it could be poor quality. There are now addons out there to help you find you rare, personally I don't see the point since, for me, the fun is fighting a pet and making a choice if it's rare or not (and when it is... yay! and if not (╯°□°）╯︵ ┻━┻) but if you find it more frustrating then fun then hunt for the addons.