Yes, you are correct with your first statement. DAT Bootcamp noted that sea urchins (widely studied) have a vitelline membrane that the sperm reacts with. I looked online and insects, mollusks, amphibians, and birds all do as well.
The word usage on all of this can be confusing so I will try to make it as clear as possible.
From outside of oocyte to the inside: Jelly coat (vitelline layer) - vitelline membrane (zona pellucida in mammals) - vitelline envelope (perivitelline space in mammals) - plasma membrane
The jelly coat (vitelline layer) is way outside of the plasma membrane. The tip of the sperm, the acrosome, first comes in contact with the jelly coat. This causes the acrosomal membrane to dissolve releasing enzymes that break down that jelly coat. When this happens the plasma membrane of the egg (below the jelly coat) depolarizes much like in muscle cells. The depolarization is the fast block to polyspermy (occurs within 10 seconds of sperm binding to vitelline layer).
In the slow block to polyspermy cortical cells inside the oocyte fuse with the plasma membrane and release Ca2+ that enters the vitelline envelope - this causes water to rush in here and increases the distance between the vitelline membrane and the plasma membrane, releasing any other sperm that could have been attached to the vitelline membrane. Also, the increased space of the vitelline envelope (perivitelline space in mammals) makes it too large of a gap between the vitelline membrane (zona pellucida in mammals) and the plasma membrane for any other sperm to bind to the plasma membrane.
