Would agree that the larger one looks like Tridacna of some kind (likely gigas). The nacreous one looks more like a piece of heavily worked shell or at best a "blister" not a "blister pearl". Serious issues with it indeed!
You can easily see that the lines of growth go straight across from edge to edge, meaning that it is most likely a piece of shell that was carved. It would be very unlikely that someone would damage a blister pearl in this way. Orient is right. Maybe it had a bump on the shell and they were trying to make it look like a blister pearl.
Let's see a close-up picture of the little round one. Try shining a spot light from above and see if any pattern shows up.