My understanding of Fourier Series was, it is a method that decomposes a periodic signal into sum of signal given by infinite number of sines and cosines. And in case of Fourier Transform it was, that it gives the function producing a signal in frequency-domain using its function in time-domain. I thought of them as two different unrelated things.
But then I came to know, Fourier Series and Fourier Transform are similar in many ways. It seems like Fourier transform decomposes the given signal too, but instead of the decomposed signals' frequency being integral multiple of fundamental frequencies, they are continuous values in a given range. And, Fourier Series is also giving us the value of the signal in frequency domain but only at certain discrete steps, and values in the middle are missing.
Are the statements that I wrote in my second paragraph correct? If not, what is it that I understood wrong?
Also, how is a method of taking a signal from time domain to frequency domain similar/same as the method that decomposes a signal into small parts? i.e. I'm confused by alternate explanations of both Fourier series and Transform that are coming up when relating them with one another. I'm seeing Fourier Series being explained in terms of method that takes gives values of a signal in frequency domain, and Fourier Transform as the method that decomposes a signal. And that is not making any sense.