I trully believe that it is a question of notation, try to figure out if the both representantion regards to the frequency domain of the signal ( Its fourier representation) if so, dont worry about each author choose his way to present the subject.
X(jw) is the frequency response of x(t). X(w) can be the same or it might be simple notatin of X(e^jw) that is the frequency response of x[n] ( discrete time signal).