Instrumentation amplifiers (INAs) are precision devices, but they have a particular function and aren’t another type of operational amplifier (op amp). Instrumentation amplifiers are not op amps; you can’t configure them in a multitude of ways, and you only set gain to a chosen value, and only within a specified range. So op amps are much more versatile than instrumentation amplifiers. An INA should never be called an “op amp,” because they aren’t and do not have the application flexibility that op amps have. INAs are precision amplifiers with a closed-loop gain over a set range.
Precision amplifiers are op amps that have better specifications and are more accurate than your average op amp. Precision amplifiers can have better specs with precision offset, zero-drift over time, lower internal noise (nV/√Hz), and input bias current. Precision op amps have precisely matching resistors etched in the substrate at the chip level. Precision op amps are necessarily integrated chips so that the components are precisely matched.
INAs do not have an external feedback. Op amps have external feedback loops that can be set by the user. INAs have excellent common-mode rejection ratios (CMRR). CMRR is a measure of the amplifier’s ability to reject signals that are common to both inputs. In this way, INAs are often used for their ability amplify differential gain, so only the signal that is not the same in both inputs is what is amplified and presented as output by the INA. Note that input impedances that aren’t well-matched will inherently cause a difference in the input signals, creating a poor CMR value. Since even precision resistors have a margin of error, it’s understandable why INAs are ideally integrated chips (ICs) where precision matching is trivial compared to matching external components. Nevertheless, you can build an INA with opamps and resistors, and INAs and op amps will have similar specifications in their respective datasheets. But an INA constructed with opamps and external resistors are necessarily inferior to an INA IC due to the problem of matching impedance.
INAs share specs like offset voltage, offset voltage drift, and input bias current. Different from the op amp’s specs are INA specs for gain error and non-linearity with respect to the INA’s gain characteristics. INAs are not op amps, but precision amplifiers that provide gain and have great difference-amplification and CMR properties.
A precision amplifier, on the other hand, could be an op amp with excellent characteristics (good specs). An INA is a precision amplifier, but INAs are not op amps, although you could make a poor INA with some op amps. A precision device of any type has better specs with lower margins of error. Precision devices that are integrated chips are qualified as precision devices when fab machines called “testers” test them. A single silicon wafer will yield a small number of devices that test as more precise or more accurate. The total “yield” of a wafer varies from wafer to wafer, and the yield of precision devices as tested product from one wafer is much lower than the total yield, of course. As such, it is reasonable to expect that precision-rated ICs will demand a premium in price.