The "Rectified Fluorescents" often come in the color industrial white like shown here: https://youtu.be/uAB4wWK2T7A

Is there much difference between those and cool white 640 or daylight 765? What's the phosphor composition?

Industrial White is a very old phosphor mix, comprising mainly the blue-emitting magnesium tungstate plus a small amount of yellow-emitting zinc beryllium silicate.  At such it has an extreme high colour temperature around 9000K, with moderately good colour rendering of 65.  Further details can be found in the links from my page on these lamps, at http://www.lamptech.co.uk/Spec%20Sheets/D%20FL%20GE%20RF85.htm