What is difference between 9.8 N (Kgwt) and 9.8 m/s^2 (g)?

The kgwt is not a unit which you should be using rather use the newton (N) as the unit of force.

9.8 crops up in a number of situations.

The force of gravitational attraction on a mass of 1 kg on the Earth is 9.8 N.

Another way of putting that is that the gravitational field strength on the surface of the Earth is 9.8 N/kg.

The acceleration due to gravity (no other forces acting other than gravity) on the surface of the Earth is 9.8 m/s$^2$ which means that all bodies accelerate downwards at the same rate irrespective of their mass - remember no air resistance etc.

One of the problems is that the symbols usually used for gravitational field strength $g$ is the same as the symbol for the acceleration due to gravity $g$.

Strictly speaking the force of gravitational attraction on a mass $m$ in a gravitational field of $g$ N/kg is $mg$ although the $g$ in that equation is often called the acceleration due to gravity.

So weight (N) = mass (kg) $times$ gravitational field strength (N/kg) although the equation will often be written weight (N) = mass (kg) times acceleration due to gravity (m/s$^2$).

You will perhaps gather from this that 1 N/kg = 1 m/s$^2$ as force = mass $times$ acceleration so $dfrac {text{force}}{text{mass}} = text{acceleration}$ which can cause further confusion because you could say that the gravitation field strength on the Earth is 9.8 m/s$^2$ and be using the correct units.