DIAPHRAGM:
We can find Diaphragm in Verticalspeed Indicator and Airspeed Indicator. I used Airspeed Indicator as the reference image. In Airspeed Indicator the diaphragm is directly connected to the pitot tube, so as ram pressure increases the diaphragm will expand and vice versa. In Verticalspeed Indicator the diaphragm is directly connected to the Static port, so the pressure inside the diaphragm directly corresponds to atmospheric pressure.
So in simple words, Diaphragm is a metal container with a small hole that will expand and contracts based on the corresponding pressure.
How Aneroid Wafer differs from Diaphragm?
ANEROID WAFER:
Aneroid Wafer is found in Altimeter. 'Aneroid' means 'without fluid'. It is not connected to any external ports because an aneroid wafer is a sealed metal conatiner where the air inside it is fixed and trapped. In altimeter, the static port is connected to the casing, the pressure inside the casing, with respect to altitude will either compress or expands the aneroid wafer.
So, an Aneroid wafer is a metal container without any hole, where the air inside is trapped.