What is the link OR difference between change in momentum & pressure difference?
It's mr Bernouilli's signature discovery: total pressure is dynamic pressure (momentum change) plus static pressure. Both static and dynamic pressure are the result of the impact of air molecules upon the wing or turbine blade, which acts as the lifting surface. The main distinction between the two is that static pressure is the result of random velocity vectors averaging zero, while dynamic pressure has an average molecule velocity unequal to zero.

Bernouilli's law can also be written as 

$$p_t = p_s + \dot{m} \cdot V$$

With $\dot{m}$ the mass of air that impacts the lifting surface per second, and $V$ its velocity. Since that is not a convenient way to make computations regarding aircraft structures, we usually see it in a format that uses air density and wing area.

There is an analogy with potential and kinetic energy. Both are forms of energy, and one form can be freely exchanged for another one. A falling object transforms $m\cdot \Delta h$ into $\frac {1}{2} \cdot \rho \cdot \Delta V^2$, but the total energy remains constant at any point in time.

The same goes for pressure, which is actually a measure of the energy of air molecules. A jet engine adds energy to the air molecules going through it. A turbine blade can be driven by either the dynamic pressure, or by the difference in static pressure before and behind the blade - there are different design blades according to the proportion of static &amp; impulse. The exhaust shape of the engine can leave the outflowing air with a higher static pressure than surrounding air, or expand the higher static pressure completely into dynamic pressure.

Static pressure and impulse change are summed together because they are two forms of exactly the same entity: the energy added to the air stream.