They are the same thing. The transient response is also known as the natural response.

transient response is due to exponential behaviour and its die with time,its not permanent.

ac transient analysis is frequency domain analysis.

The slowest poles of a system (those closest to the imaginary axis in the s-plane)

give rise to the longest lasting terms in the transient response of the system.

if a pole or set of poles are very slow compared to others in the transfer function,

then they may dominate the transient response.

If we plot the transient response of the system without accounting for the transient

response of the fastest poles, we may find little difference from the transient

response of the original system.

decays