The Eternal Tiare was the weapon Sailor Moon received when she became Eternal Sailor Moon. It was used to perform Starlight Honeymoon Therapy Kiss and Silver Moon Crystal Power Therapy Kiss.
In the manga, the Eternal Tiare appeared when Usagi gained the power to transform into her Eternal form and it was never upgraded. It was broken in Act 50 when Sailor Moon fought the Sailor Senshi under Sailor Galaxia's control, but she recreated it shortly afterwards with no apparent difficulty.
During the final "Chibiusa's Picture Diary", Sailor Chibi Moon also had an Eternal Tiare. However, she was never shown to have it during the main storyline.
In the anime, the Eternal Tiare first appeared in episode 167. It was formed from the Kaleidomoon Scope when the nine other Sailor Senshi, at Sailor Saturn's request, gave their powers to Sailor Moon, allowing her to attain the Eternal Sailor Moon form. The change of appearance became permanent when Usagi learned to transform directly into Eternal Sailor Moon without going through the Super phase first.
The Eternal Tiare became the Moon Power Tiare when the Holy Moon Cálice attached to it. The chalice was never named during the series and played no role outside of the attack.