What is the meaning of the difference between the Fourier transforms of a single pulse in these two cases?
The differences:

1) Your pulse starts at t=0,5 seconds. The pulse in the printed book starts at t=minus half of the pulse length

2) Your spectrum discards negative frequencies and phase angles. It shows only the magnitudes of the components at positive frequencies. The spectrum formula and also the graph in the printed book are exact, they have magnitudes and phase angles and give them at positive and negative frequencies. Just this lucky case - a symmetric pulse around t=0 kills all imaginary numbers in the spectrum, one curve and the imaginary unit j nowhere in the formula.

3) If you zoom in your spectrum, you see it's discrete. It contains only frequencies N x 1/total sampled time period. N is integer and the covered frequency range is 0...half of the sampling frequency. The exact spectrum in the printed book is continuous in frequency domain. The printed spectrum formula covers all frequencies from -infinty to +infinity

You may ask how FFT spectrum would still be errorneous if the phase angles and negative frequencies were added. Answer: It would give the same pulse infinitely repeating. The repeating period is = the total sampled time period. That is not considered harmful because the user of the spectrum should know that only one pulse really existed.