Hi there,
ZIR zero input response is the response to internal excitations only.
ZSR zero state response is the forced response to init conditions of 0.
The transient response is the superposition of both of the above. Kind of a fancy way to explain that the total response depends both on inputs and internal states, and also that the internal states work sort of like inputs of their own.
The steady state response is the response at t infinity after all the exponential terms have stabilized. Note that at t infinity states could be whatever the circuit settled to, either zero or non-zero, or even sinusoidally changing with time.