StephaneLamy: [current position]
In this position, A18 seems equivalent to B18.
The natural follow ups B18E19A18 and A18E19B18 just interchange the order of these two moves.
caranthir: I think the move orders have qualitative differences. 1) If we play A18, then E19 remains a ko threat (which the opponent should of course not play right away as in the problem sequences.) 2) When we play B18 instead, now this is sente unless there's something bigger elsewhere than the entire corner - and after E19A18, there are zero ko threats against us in the position. 3) If it's not sente, then later we may capture the three stones and in that case, had we played A18 also, that stone would become wasted. -- All that said, both options should be accepted in this problem considering the overall level of the collection.
JPortman: Maybe it will be a good idea to add one more possible response for the capturing side? I mean, in some problems we see a message "Correct, but what about this move?". So in this problem after the first move from the defending player (B19) the capturing player responds with B18 - the strongest response possible. But he can also respond with C19 - a slightly weaker response, but still a sente. And the defender will have two possible moves: A18 or B18 (both give him two eyes, but one is sente and another one is gote). What do you think?
I think the move orders have qualitative differences. 1) If we play A18, then E19 remains a ko threat (which the opponent should of course not play right away as in the problem sequences.) 2) When we play B18 instead, now this is sente unless there's something bigger elsewhere than the entire corner - and after E19 A18, there are zero ko threats against us in the position. 3) If it's not sente, then later we may capture the three stones and in that case, had we played A18 also, that stone would become wasted. -- All that said, both options should be accepted in this problem considering the overall level of the collection.