intensity scaling: precise definition?
Intensity scaling can be just as you say: multiplying all intensities by a scalar value. This will obviously change the histogram, but will do nothing like histogram equalization (it will just scale the x-axis of the histogram, barring some binning effects).

More generally, intensity scaling can change the range of intensities so that instead of going from $\tt x_{min}$ to $\tt x_{max}$ the pixel values range from $\tt x_{new\ min}$ to $\tt x_{new\ max}$ that might be better for display purposes (e.g. $\tt x_{new\ min} = 0$ to $\tt x_{new\ max} = 255$ or $\tt x_{new\ min} = 0$ to $\tt x_{new\ max} = 65535$).

See Gozales, Woods, and Eddis for example.