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A two stage amplifier is an amplifier whose gain is divided between two stages. this way, the specs for each stage become less intense making the design possible.
It is totally different approach to design a amplifier and a comparator.
The key point is, in my opinion, comparators are open loop circuit and there's no need for compensation, which is really important in amplifier design...
It depends on where and how you put your ampllifier. If you put in a closed loop configuration, you have to concern stability issues. If it's open loop configuration like most comparator is used, it simply amplify your inputs until it saturate.
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