Is Fourier series a sampled version of Fourier transform?
There are 4 versions of Fourier transforms that are all close cousins. 

It's all due to the basic property that "sampling in one domain corresponds to periodicity in the other domain". If a time signal is periodic, the frequency domain signal is discrete. If a frequency domain signal is periodic, the time domain signal is discrete. 

So you have four variants

&gt; `Time                       Frequency               Transform 
Continuos &amp; aperidoc          Continuos &amp; aperidoc    Fourier Transform
Discrete  &amp; aperidoc          Continuos &amp;  peridoc    Discrete Time Fourier Transform
Continuos &amp;  peridoc          Discrete  &amp; aperidoc    Fourier Series
Discrete  &amp;  peridoc          Discrete  &amp;  peridoc    Discrete Fourier Transform


The flavors are different since a continuous signal requires integration and a discrete signal needs summation.

The naming conventions are non-intuitive: it would be easier if the DFT would have been called Discrete Fourier Series and the DTFT called DFT, but it is the way it is.

Which flavor you need to use depends on the nature of your signals and depending on what assumptions around the signals you can make, you can use one flavor to calculate a different one.