How can the I and Q components of a quatrature signal be different from each other (apart from the 90º phase shift)
You are mistaken in your 2nd paragraph.  The I and Q components are not always identical with a 90 degree phase offset.  Instead, they are usually generated by multiplying some real or complex signal with two sinusoids that offset by 90 degrees.  Only if the input is a constant (e.g. carries zero information) does the IQ output fit your description.

A strictly real signal has no imaginary component.  But when heterodyne modulated (complex multiplied) by a complex carrier (two higher frequency sinusoids, cosine and sine), the result is a complex IQ signal.  If the baseband signal is not just strictly real, but complex, the result of that heterodyne modulation can produce completely independant and unrelated I and Q components in the IQ result.

When down-converting a higher frequency strictly real signal to baseband, again you will get identical I and Q with a 90 degree offset only for constant input.  But if the real input is not constant, but varies over time, the complex multiplication result can produce very different I and Q component waveforms.  This is because the local maxima of the cosine waveform and sine waveform occur at different points in time, and thus can be multiplied by different input values if the input is varying, thus producing in different result values, thus making the waveforms different, not just offset by 90 degrees.

Since QAM can carry information (e.g. not just a single constant value), the I and Q components can vary.