Hi,
I had the same questions (and more) a while ago, about IQ.
I'll give it a try and any correction is highly welcomed!
No, they don't have to transmit identical data.
In QAM modulation, the IQ signals modulate the amplitude and phase of a carrier (RF signal).
I and Q are two different signals, orthogonal to each other, so there is no interference between them.
Suppose it is I(t)=a(t)*cos(θ) and Q(t)=a(t)*sin(θ).
Cos and sin are orthogonal, since they have pi/2 phase shift with each other.
The final QAM signal is just the sum of the I/Q signals:
x
qam = I(t)*cos(w
c t)-Q(t)*sin(w
c t),
where w
c is the carrier frequency.
This x
qam signal is called a "symbol".
In 4-QAM, there are 4 possible symbols (waveforms), each "carrying" two bits.
The bits 0,1 are just two voltage levels, that show the amplitude of each I/Q signal.
Changing the amplitudes of IQ, changes the amplitude and phase of the final RF signal,
resulting in a different symbol.
In higher orders of modulation, 16/64 QAM, each symbol "carries" 4/6 bits.
In these cases, you just have more voltage levels (I/Q amplitudes), 16 in the first case, 64 in the second.
Now, regarding how the bits are separated in IQ, I think this has to do with the mapping you use.
As an example from real life, PSK31 is a digital communications scheme,
that uses the I signal for the information data and the Q signal for the error correction coding data:
https://www.arrl.org/psk31-has-rtty-s-replacement-arrived
This is mentioned in the section "From BPSK to QPSK".