as far as i understood the question, here is the answer:
1. both 1 and 2 are same circuits i.e. op-amps configured as comparator except for the input type, both are step inputs except for one has discontinuous change from 0 to Vdd and another has ramp (continuous) change.
2. Almost most of op-amps have very high open loop gain, for eg. uA741 has open loop amplification rate of min 20V/mV and typical 200V/mV. so, even a small diff in voltage will drive op-amp to its rail. Im not sure how did u actually calculated two gains, the only thing i can think of op-amp with no rail to rail o/p.
3. Also, if u use circuit in negative feedback configuration then only the gain changes based on ur feedback component values.
4. In comparator mode, gain is never considered as parameter for app design.
Hope that helps.