Is Step the same as an Impulse + 1/s? Isnt a Step (as a Transfer function -&gt; $ \frac{1}{s} $) and Impulse (trans fcn -&gt; 1) therefore Impulse + $ \frac{1}{s} $ should be equal to a Step in Simulink right?
I made a Simulink model:

But the outputted plots are not the same ?
Why is that? Am I wrong? Should those two blocks be essentially the same?
The problem is that you can't use a Dirac delta impulse as an input, which would be the theoretically correct thing to do. Since you only have a discrete impulse, which has some finite value, and since Simulink probably uses something like a zero-order hold to make a continuous-time signal out of that impulse you actually use two different input signals: a step and a smoothed step.