What's the difference between a microphone and a barometer? A barometer is a device that measures air pressure
A microphone is a device that detects sound waves. Sound waves which travel through air.
Pressure of a gas is caused by the motion of the gas.
So, a barometer measures the motion of air, and a microphone measures the displacement of air, which seem to me like the same thing, so what's the difference?
 A: You're correct that in both barometers and microphones air pressure changes are converted into displacements and those displacements may be converted to electrical signals.
We can think of them both as pressure sensor devices that define a function $x(P(t))$ where $P(t)$ is the pressure at the device input over time $t$ and $x$ is the position displacement of the sensor.
From a signal processing perspective the differences are:

*

*A microphone has a much larger bandwidth. That is, high frequency (e.g. acoustic) pressure fluctuations will not turn into noticeable position fluctuations for a Barometer. Barometers work at very low frequencies (probably Hz bandwidth at best? I don't know,) while microphones work at acoustic frequencies. The comments indicate that some microphones have finite response at DC while some don't.

*The operating ranges are much different. Barometers will report pressures down to pretty low pressures and up to high pressures relative to atmospheric pressure. The displacement of a microphone sensor will clip very quickly if the pressure changes too much from atmospheric pressure. This is related to the the dynamic range of the sensor devices.

*The sensitivities are different. Microphones can detect very small pressure changes (at the appropriate frequencies) whereas barometers cannot. (similar to last point)

So yes, both barometers and microphones use displacements to measure pressures. But as sensors they have vastly different specifications. That said, since they're both pressure sensors, I'm sure technological developments in barometers have influenced microphone designs and vice-versa.
A: A barometer measures the absolute pressure. It cannot follow the pressure change arbitrarily fast. That means it has some upper cutoff frequency when regarded as a measurement device.
A microphone considered as a measurement device, on the contrary, also measures pressure, but not absolute pressure. It has a lower cutoff frequency and can only detect deviations of pressure from the average pressure. If the changes are too slow it cannot detect them and is completely immune to slow changes in the base (ambient) pressure. Fast enough changes are detected though (and this is "sound").
Note the other answer dp/dt is not correct, as there would be a strong frequency dependence. Double frequency would generate double electrical signal. This is not the case for a microphone.
A microphone is supposed to generate an electrical signal proportional to the acoustic level which is the pressure level.
To be fair, the frequency response of a microphone is not supposed to be flat but follow some characteristic to mimic human ear. But this is not dp/dt either.
A: Mathematically  stated,  the difference is that a barometer detects  an average of  the  variable, $p$,  and a microphone  the $dp/dt$ . See the illustrations in this link.

A: There is at least one design of a microphone and a pressure sensor that really differ only in geometry:
The carbon microphone:
https://en.wikipedia.org/wiki/Carbon_microphone
...
and the rarely-used these days carbon powder pressure sensor (I really can't find a good webpage, but take my word that these do exist and I have one in my 1982 car).
The only difference between the two is the mechanical design and, of course, the field of application. The principle of operation is the same.

Now I am curious, if I attach a speaker to the oil pressure sensor, will I hear the sound of the oil pump teeth?
A: There are several different technical solutions to microphones which influence what they measure. I will limit this discussion to two types: an omni pressure sensitive mic and a figure 8 velocity sensitive mic.
First the figure 8 microphones which does not measure air pressure but instead air velocity: Imagine a very thin not very wide ribbon or band set in more or less free air, suspended from its both ends. (This is actually a rather good description of how a ribbon microphone is created. Typically a very thin alumnium band, say half a centimeter wide and 3 centimeters long). The band will waver to and fro depending on the velocity of air "wind". We can call this that the band acts according to local air velocity. As sound is "wind" going to and fro here, the mic then translates this wavering motion into an electrical signal. You can understand that the air pressure, barometric pressure, is more or less same on both sides of the band. The mic will not react to high or low air pressure. This mic will be sensitive to air movement perpendicalur to the surface of the ribbon, but quite unsensitive to air movement over the thin band creating a sensitivity graph looking like the number 8, hence the name.
Now for the second type of mic I talk about here: an omnidirectional pressure sensitive mic. Imagine a thin membrane tensed across a closed cavity. (Again, this is actually the design of mics and some barometers). Increasing air pressure will push the membrane in towards the cavity, decreasing air pressure will allow the membrane to move outwards. Sound is seen here as a local to and fro in the pressure of air. The mic (or barometer for that case) translates this into an electrical signal. For barometers, the cavity may be fixed reference, say a vacuum. For actual microphones though there is a small hole from outside air to the cavity. This will allow the cavity to be filled with air around with on average the same pressure as outside air. In effect the hole will work as a high-pass filter: only air pressure variations with a high enough frequency can be registered by the mic. The "barometric" pressure, of a very low frequency, will hence be filtered out and only the higher frequency sounds will remain. (Now, some measurement mics may go below 1Hz as lower frequency, but mics used for recording music usually starts at something like 10Hz as there is very little music in lower frequencys). The pressure measuring mic is more or less omni-directional on lower frequencys (same sensitivity in all directions) but will become more and more directional in higher frequencys (say above 1kHz) due to the exact design as the membrane does point in one direction.
As a side note: most microphones used for voice or music today have a cardoid pattern. This can be though of, and sometimes created, a combination of omni + a figure 8. Exactly how to do this is left as an exercise for the reader ;-) .
A: Both are monitoring air pressure, but they are far from the same thing.  One is designed to pick up tiny, fleeting fluctuations with great precision, while the other is designed to read out a stable number.  Sort of like your ear vs an achey joint, or a voltmeter vs an oscilloscope.
If you made a sufficiently lightweight barometer and amplified its output, you would have a microphone!  However, you couldn’t necessarily use the output of just any microphone to determine the atmospheric pressure, because all that determines our perception of voices and music is how the pressure oscillates, not its average value.
