What is the difference between a Line Impedance and Charecteristic Impedence?
I think, when the voltage is incident on the PCB trace, we are
considering 'Impulse Response' of trace. Correct? Please correct me if
I am wrong

The characteristic impedance (\$Z_0\$) can never be held constant across a range of frequencies for any signal because, (for instance) a typical digital signal can encompass DC and high frequencies. Basically at DC \$Z_0\$ has one value and at HF has another value: -
$$Z_{0(DC)} = \sqrt{\dfrac{R}{G}} \text{  and  }Z_{0(HF)} = \sqrt{\dfrac{L}{C}}$$
For audio there is the usual in-between value based on R and C being dominant: -
$$Z_{0(AUDIO)} = \sqrt{\dfrac{R}{j\omega C}}$$
Important for maintaining signal integrity is what happens at the end of the transmission-line and that is called &quot;matching&quot;. We match with an equivalent impedance so that reflections don't occur. Reflections happen because the power travelling down the transmission-line arrives at the end, and the impedance doesn't match the V and I waves of the power sent. The net power mismatch can only bounce backwards.
For very low frequencies this doesn't matter but as frequencies get higher, this problem gets progressively worse and, as a rule of thumb we say that as the length of the transmission-line gets within one-tenth of the wavelength of the signal it transports, we should consider terminating the transmission-line with an appropriate impedance. This prevents reflections that can disrupt the integrity of the signal or cause what are known as standing waves.
I've never heard it called &quot;Impulse response&quot; but I wouldn't be surprised if it's OK to do so. But there are broader reasons just to refer to it as &quot;matching the line impedance&quot;.

How and why do still we maintain the trace impedance?

Why - to avoid reflections disrupting a signal or causing it distortion that is unacceptable.
How - Trace width modification, trace-to-ground-plane clearance and dielectric constant of the PCB material.

If you have any good study material that would be great too!

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