Lavitz

Similar description, so could both be the same type of gemstone? With a spren trapped inside?

Sorry if I missed it, (lot pages on this thread already), but in the WoK prologue, Gavilar gives a stone to Szeth, which seems like the same type of stone that he gives to Eshonai. Did I miss something? Or was Gavilar just handing out these stones to everyone? I assumed he only had one.