This is the best comparison photo I’ve seen and to me they are clearly not the same necklace:
https://hosting.photobucket.com/ima...riginal.jpg?width=1920&height=1080&fit=bounds
https://mb.boardhost.com/historyroyaljewels/msg/1576127076.html
To add to my list, they also have the emerald, pearl and diamond belt from the Maharaja Sher Singh:
https://www.rct.uk/collection/11291/emerald-girdle-of-maharaja-sher-singh
And Princess Diana was photographed in what looks like an emerald necklace, which would be with her sons now:
http://www.dianasjewels.net/Earrings/PaveEarrings-Necklace1.jpg
There are also reports that the Queen received an emerald and diamond necklace as a wedding present.
I mean, we truly have no idea what’s in the vault. Look at Sophie’s 3 tiaras, we don’t know where they come from and why they haven’t been worn more. The Greville Double Meander was also only worn once by Anne and there’s Eugenie’s wedding tiara never before worn, etc.
It’s quite possible that there are gifts to Queen Alexandra, Queen Mary and the Queen Mum still never worn in public or photographed. In those days the royal women were literally showered in jewels whenever they made visits or went on tour, both official and private.
I am also sure that Catherine received a nice haul for her wedding, but she wears it very sparingly.