Regarding demons with the same name but different base rarity, they are recognized as the same demon and as such are not able to be placed in the same party.
Special Aethers are required.
Bayonetta Collaboration Characters: 「Witch Aether S」 and 「Witch Aether L」
DMC5 Collaboration Characters: 「Soul Aether S」 and 「Soul Aether L」
In regard to the details of the other collaboration characters, they are listed in the links below, please do verify them altogether.