Yes, in the traditional manner, on wild sturgeons.
On farmed sturgeons, a cesarean delivery is now used, with the eggs being removed and the fish being kept alive so that more may be produced the next year. They require even ten years to produce a mature sturgeon, thus this strategy provides a greater financial return.
Sturgeon flesh, by the way, is delicious. (In the 14th century, Chiquart wrote, “Esturgeon est 1 poysson Royale!”)
To begin, caviar refers to roe or egg. Yes, and caviar refers to the eggs found solely in sturgeon fish and not in any other fish.