Indeed there is a difference.
In your sensor example, the amplifier works on the voltage it receives from the sensor. So it makes sense to maximise the voltage by using a high input impedance amplifier.
Likewise sensors like photo diodes output a current that is proportional to their input (light for example) so then it makes sense to maximize the current by using a (current) amplifier with a low input impedance: the Trans Impedance Amplifier.
Both cases above achieve maximum power mismatch. Yes MISmatch! But that is on purpose to maximize the voltage or current.
Power matching is mostly done when we need to maximize the power transfer. An example of this is a device which delivers a certain power and will only deliver that if the load has the correct impedance.
A low frequency example is an audio power amplifier. If the audio amplifier can deliver an undistorted signal of up to 10 V, 2.5 A, what load impedance would result in maximum power? Simply apply ohm's law: 10 V / 2.5 A = 4 ohms.
That results in 10 V * 2.5 A = 25 W.
If we loaded that amplifier with an 8 ohm speaker, the voltage is the limiting factor: 10 V / 8 ohms = 1.25 A which equals to 12.5 W
(at 2.5 A through 8 ohms, we need 2.5 A * 8 ohm = 20 V => outside the 10 V limit)
If we loaded that amplifier with a 2 ohm speaker, the current is the limiting factor: 2.5 A * 2 Ohms = 5 V which equals to 12.5 W
(at 10 V across 2 ohms, 10 V / 2 ohm = 5 A would be needed => outside the 2.5 A limit)
Another example is an RF transmitter feeding power into an Antenna. To avoid signal reflections (explained below), RF power amplifiers have a certain output impedance, they need to "match" the cable's characteristic impedance. Also antennas only work properly (minimal reflections) when they are matched to their cable. You might think an antenna is "just a piece of metal" but there's more, it is actually an electrical interface to the air. This air also has an impedance just like the cable feeding the signal to the antenna. All these impedances need to be such that no reflections occur.
There is another reason for power matching, when we use RF signals it is possible that the wavelength of the signal comes close to or is smaller than the dimensions of the conductors (cables etc.) we use. Then conductors and cables behave like a transmission line.
A transmission line must be terminated properly to avoid signal reflections. Signal reflections disturb the signal, they distort it. Proper termination (the right impedance at both ends of the transmission line) is needed to avoid reflections and allow for undistorted transportation of the signal.
This is why many coaxial cables have a "characteristic impedance", for example 50 ohms. The cable does not "have" this impedance (you cannot measure it with an ohm meter) but
you do need to terminate the cable with 50 ohms at both ends to avoid reflections.
As mentioned, this only applies when we use signals which have a wavelength which comes close to or is smaller than the dimensions of the conductors. For most sensors this is not the case, the signal does not change rapidly, it is a low frequency signal. Therefore it has a very long wavelength (can be hundreds of meters long) and reflections are not an issue.