To be honest, I feel like there's no dependence between care and the character you get. With perfect care I got Neotchi->Coffretchi and with bad care it was the same.
Maybe I'm doing something wrong? Is the "bad care" letting your tamagotchi be close to death? (I'm sorry but Tama Friends is...
I don't think it's only for marriage. In TF manual ( https://uk.tamagotchifriends.com/wp-content/uploads/sites/3/2013/11/TAMAGOTCHI-DIGITAL-FRIEND-INSTRUCTION-SHEET1.pdf ) you can clearly see that "special" is for "bump with Special Retailer KIOSK and get jewelry including exclusive ones"...
When I read about TF on forums I feel happy I don't have comparision with the older versions - I never had an original tama before TF :P Well, if you look for something that reminds you about childhood, when you played with fake tamas, TF is perfect because the design and gameplay feel SO much...