Lean idle. Rich cruise.

Modern gauges should all read the same to within a tolerance that is small. A modern wideband sensor comes paired with a calibration module in the plug connector. they etch off a chunk of some resistor or chip in the plug connection section to get it calibrated
that connector and sensor are now paired for life

usually a warning sticker saying do not disconnect this bit disconnect the wire at the other end of this part with the flip up clip weather proof connector

what happens is someone then takes 1 sensor ignores the warning sticker or it comes off and then swaps the connector bit along with the wire to another sensor and you end up with something that is way way out
i.e you have 3 parts
the wire harness
the plug bit
and the sensor that bolts into your headers

The majority of the plug bit is married to the sensor and is there to provide calibration BUT can be removed if you are persistent enough

most of the screw in wideband sensors will be bosch or similar these days and they do put effort into getting it right. when they make the sensor they don't know if its going into a aftermarket kit or its going into a box of 5000 to be delivered to Peugeot/FIAT :) for the challenger production line, they all need to be calibrated correctly because the ECU they usually connect to, expects them to be.

AEM and similar all use a chip and LED based gauge, again the tolerance stack up in the circuit will be tiny and inconsequential.

in the past or with unknown history, or cheap knock-off/fake ..... ????

new stuff as in last 10-15 years should be pretty accurate

Dave