How can the I and Q components of a quatrature signal be different from each other (apart from the 90º phase shift) I've spent many hours reading and doing research about this. I don't attend any university classes or any type of classes that may approach such a topic. I am trying to learn this by my own without any help what so ever. So please understand if I say something inaccurate or if I'm asking an obvious question. I have been studying quadrature because I need it to develop in software defined radio platforms. The problem is that I have found a lot of contradictory information.

Let's start from the beginning. Given a real signal to a quadrature circuit, two components are generated, I, the real component, and Q, the imaginary component, which is the same as I, only it has a 90º phase shift. So, we have I and Q, which are the same signal but 90º shifted from each other. I understand this, it's simple.

Now let's see an example. Have a look at this paper about QAM on ni. I read the paper and I understood it. The problem that is if you take a look at the baseband graph, the I and Q components are completely different. They shouldn't, right? They should be equal to each other apart from the 90º phase shift. At least that is what I understood after reading many papers and articles on the subject.

Now let's take a look to this article about IQ on tek. Having a look at the last two images, I can visualize what's happening. The I and Q are being transmitted and then received. I can see that the I and Q components transmitted are the same being received. What I don't understand is that Q isn't by any means equal to I with a 90º phase shift. That is what's supposed to happen right? Maybe not? I can't seem to understand it. I know that the I is obtained by multiplying the real signal by 2cos(w(c)t) and that Q is obtained by multiplying the real signal by -2sin(w(c)t). So, what I saw before clearly makes no sense.

Again, I'm sorry for my ignorance in the subject but I am doing my best trying to understand this. I'm just confused by this contradictions. Thanks in advance for anyone who tries to explain this to me, really.
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.