Do faders & potentiometers basically work exactly the same way just laid out differently?
Yes. Metal ‘wioer’ conductive track. Straight or circular. Old tracks were soft carbon which was easily damaged, So easily damaged they usually had a metal disc which tilted and it was that which the metal wiper touched, pushing it into contact with the track. Yours are probably carbon about newer and tougher but still possible to damage.
Faderlube deoxidises and lubricates and will only clean in the sense that it occupies the microsooic space between wiper and track and is ‘clean’ and bridges gaps between and around the dust but doesn’t actually clean. A little shot of compressed air then contact cleaner first if necessary.