I have always considered a "pet" to be a reverent term for a 24/7 type slave for whom I have genuine affection for.. Also, a pet will act like a cute, affectionate "pet".. Wag their bottom (reminiscent of a puppy) when excited, lick Mistress'/Master's hand to show affection and nuzzle My leg when on all fours/crawling (etc.)..
I have fuck-pigs (cumsluts) who I may call "piggy", which I consider to be a sort-of cutesy affectionate form of address.. But I can't say I've ever called 'em pets..
Hmm.. Interesting..