Each type of film has a specific ISO speed standard.
The one most of us are familiar with applies only to B&W
negative for use in still cameras. Negative for motion
picture use is measured by a different standard.
    I don't have a copy of the current standard for color
negative film but there is at least a partial description in
(1). This states that the speed is measured by finding the
log of the exposure in lux-seconds for the "minimum useful
density", given as 0.15, for the Status-M green curve and
the lowest of the three curves (usually red) and averaging
them. The speed is then:
Speed = 1/Hm x 1.5
    My reference does not state if there is a specified
gamma for the measurement but color negative films generally
have a gamma of around 0.5 to 0.6.
    Note that the Log density of 0.1 is not exactly the
speed point for B&W. The ISO standard includes a 1.5X
multiplier. This is to move the minimum exposure up the toe
to a point where the toe gradient is sufficient to provide
good shadow detail. The B&W standard specifies processing
conditions which are not standardized as they are for color.
I expect the color standard probably also has some
specification for dye density range and gamma.

1, _Photographic Materials and Processes_ First edition,
Stroebel, Compton, Current, Zakia  Boston, 1986, The Focal
Press ISBN 0-240-51752-0