No, this is not what people mean when they say "Fourier series" which is something like "the Fourier series expansion of a periodic function". It's not about w

No, this is not what people mean when they say "Fourier series" which is something like "the Fourier series expansion of a periodic function". It's not about whether the values are continuous or discrete, but instead about the domain over which the values are defined. Fourier series maps a periodic function over a continuous domain into a countably infinite number of coefficients.