Physical difference between ISO and gain
ISO stands for the International Standards Organization.  They standardize all kinds of stuff, including film stock for photography, cinematography, and digital video.  If you're using a digital camera that uses ISO instead of gain, then it should conform to the specifications they've outlined in ISO 12232:2019, which is available for purchase here.

There's a very good wikipedia article on the subject here.

Gain is just the amount of amplification in decibels that the camera applies to the signal from the sensor before it gets recorded to the image.  Some cameras apply gain before analogue to digital conversion, some apply it after, and some, such as the BlackMagic Pocket cinema cameras do both, to achieve what they call, "dual-native ISO."

So, in short, Gain is a measurement of amplification, and ISO is a standardized measurement of film/sensor sensitivity.  Gain does not necessarily correlate consistently to exposure across different camera makes, models, and manufacturers.  It's just a "volume knob."  ISO is designed to correlate to exposure universally (but it does not consider some variables and imperfections, which is what EI does, similar to the difference between "T stop" and "F stop" measurements for aperture).