Re: DSP
The difference is in that continuous time Fourier series are used to represent periodic signal (the spectrum of such signal is discrete, that's why Fourier series consist of separate harmonics). Conversely, continuous time Fourier transform represents aperiodic, unlimited (in time) signal (which have continuous spectrum).
By the way:
Fourier Series: periodic, continuous in time domain -> aperiodic, discrete in frequency domain
Fourier Transform: aperiodic, continuous in time domain -> aperiodic, continuous in frequency domain
Discrete Time Fourier Transform: aperiodic, discrete in time domain -> periodic, continuous in frequency domain
Discrete Fourier Transform: periodic, discrete in time domain -> periodic, discrete in frequency domain
That is, a periodic signal has discrete spectrum, an aperiodic signal has continuous spectrum, a discrete signal has periodic spectrum and a continuous signal has aperiodic spectrum.