With the FFT you are attempting to approximate the FT of a continuous function using discrete sampling for a finite time. The approximation is "perfect" when the continuous function is bandwidth limited. The Rectangle function is not, you require an infinite number of terms in its Fourier series approximation.
A simple way to imagine the relationship between the finite sample on which you are going to perform the FFT and the continuous function you are approximating is to periodically extend the finite sample in positive and negative time. When you put in a simple rectangle pulse into the FFT you are seeing the approximation to the FT of a square wave with some duty factor, not of a single pulse. This probably explains most of the confusion.
The details of the relationship between the FT of a continuous function and the approximation via a discrete FT is detailed and subtle and you should probably study a signal processing or mathematics textbook.
