I seriously doubt the ability for a pet to pick up drops on its own is limited to certain kinds of pets. If you spend real $$$ on a cash shop item, aka the one in the original image posted in this thread, then your pet - regardless of kind of pet - will walk over to pick up your "spoils" and monster "leftovers" without you having to lead the pet over to the area in which those items/mesos are located.
Regarding pets' skills, if your pet reaches a certain level it will have new commands, aka the "/pet" at level 15, and the highest level command(s) by level 20. Some pets have more commands than others but not many, usually only one or two. With other pets you gain "closeness" faster in the pre-level-10 commands. My tiger gains more closeness points in lower level commands than my mini-kargo.
Zylek (with L), Fighter (almost Crusader!) - Broa
Zylek (with i), Cleric - Broa
ZyleksMule, level 1 mule - Broa
Drakahn, n00b-Assassin - Scania
Drahk, n00b-Bandit - Mardia
Mardia~OddPhive lvl 43 Brawler (Semi-Active)
Mardia~MetalicPhive lvl 52 Bandit (Frozen)
Scania~NenoPhive lvl 91 I/L MAGE (Frozen)
Scania~SpellSword (SpeiLSword) lvl 40 STR Cleric (Frozen)
i came across 3 ppl w/ the 'pick up leftovers' thing in 1 day, in broa, one was afk... one said it worked and one said it did *not* work.
weird.
and for the 3rd time, we KNOW what it is lol.
Zylek (with L), Fighter (almost Crusader!) - Broa
Zylek (with i), Cleric - Broa
ZyleksMule, level 1 mule - Broa
Drakahn, n00b-Assassin - Scania
Drahk, n00b-Bandit - Mardia