I believe there is an issue in the interpretation of the F in CTFT. FT stands for Fourier Transform. Each of the dual variables time and frequency can be either continuous or discrete. The Continuous-Time Fourier Transform (CTFT) is often simply called "Fourier Transform", and uses both continuous time and frequency. For the Discrete-Time Fourier Transform (DTFT), time is discrete, yet the frequency is continuous (with inherent periodicity).
Other avatars are Fourier series (continuous in time, discrete in frequency) and the Discrete Fourier Transform (DFT), discrete in both domains. All of the above have subtle relationships, and share a handful of similar properties. In fact, CTFT is not piratically usable for computations, and DFT (and FFT) are best efforts to turn CTFT into something usable.
So I am not sure that "continuous-time frequency" is meaningful by itself. It might be a short-hand for "continuous in time (and) frequency".