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Honestly,you should read some signal processing theory for this.There are so many concepts here.Information which can be extracted from both domain is different.Fourier transform is a mathematical tool used to convert time domain signal to frequency domain.Signal which is time limited in time domain is frequency unlimited in frequency domain and vice versa.Also Parseval's theorem says that energy/power computed in both domains is same.
Foe example Impulse signal in time domain has fourier transform 1.This signifies that this time domain signal which is there for fraction of time will affect all frequencies.This you might have observed in your household..if you turn on/off tubelight then there is some fluctuation for a fraction of time with radio also.
For more info read Signals and systems book written by Oppenheim
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