Circuit (a) is simply a voltage follower unity gain with AC coupling due to effective input resistance R ( big) and series input Cap, C , T=RC. THe result is DC or low frequency blocking and output will be at same DC voltage as (+) in this case ground.
Circuit (b) is an AC divider amplifier just like a resistive divider amplifier except it has no DC reference so additional circuits must switch the feedback cap to null any offset. THis design is used for piezo capacitive accelerometers where the charge generated from vibration is amplified by the C ratio (Cin/Cfb) and presents a high impedance to the piezo device.
I have no idea what the author was trying to demonstrate for (a) as sampling mode because there is no sample and hold switch.
In (b) the amplification mode is shown for the step response but actually the input RC filter response for the input bias current and effect resistance and hence LPF effect shows the time response, but above this frequency breakpoint the AC frequency response is flat gain.