what is a unit sample response ? It is denoted by h(n) , is it same as the impulse response?
It's not the same because they are defined in different signal presentation systems. Unit sample response is meaningful in discrete time systems, impulse response is a valid concept for continuous time systems.
The unit sample response assumes input sample sequence u(n)=1,0,0,0... or more formally u(n)=1 if n=0, u(n)=0 for other integer n values.
NOTE: also negative n is often allowed in DSP math books for nice symmetric formulas. In that case u(n)=...0,0,0,1,0,0,0,... where 1 is the sample number zero.
Both have same purpose - to characterize exactly how a linear system affects signals without telling anything of how the system is constructed and what suboperations it uses to do its work.
Without diving into exact math i must tell that the unit step response resembles a sampled impulse response visually when drawn for 2 systems which are designed to do the same practical thing - one in DSP and the other as RLC circuit. Sampling a continuous time impulse response is one, but often less than optimal way to create the wanted response for a same doing DSP system.
I have tried to make a room-like reverberation filter by recording digitally the sound in a room when one sharp hit was made with 2 quite hard woodblocks. That recording was used as the unit step response of my fake reverberation filter. It worked but the sound of the used blocks were a part of the result.