When we were on Mount Teide a few years ago, my husband bought me a ring with volcanic stones in it (green olivine and black obsidian). It was nice to choose a ring with volcanic stones in it while standing on an active volcano!
Olivine is essentially the same mineral as peridot, but the word peridot is normally used to describe gem-quality stones. Another way to explain it is to say that olivine is the mineral form of the gemstone peridot, olivine being the name of a group of minerals that contribute to rock formation. I had not heard of olivine before visiting Tenerife, and had only heard of peridot.
Peridot is the birthstone for August and the anniversary stone for 16 years.