This is a most beautiful set. The descriptions I have found online state that it is likely a “natural sea or bamboo coral”
I have had this for a long time and it is real coral that much I know as it gets nice compliments whenever I have worn.

Tiny sterling silver tags on both items.

Features large, irregular coin-shaped natural beautiful stones. These are polished with a high sheen. The necklace is tied between coral with red cording. The clasp on the necklace is sterling silver floral and so pretty. The bracelet matches and has a small sterling silver spacer between each piece of coral.

Measures Necklace Length = 10” inches
Bracelet measures = 4” inches long - 2.5” round
Styles - This aesthetic is frequently categorized as boho-rock, tribal or statement jewelry.
It is also common in Native American Navajo handcrafted designs.

I love the imperfectly perfect coral chunks they are beautiful.
I have had this in my collection and just love seeing this coral. I bet you will enjoy wearing and seeing it as well.