In your opinion, does each pair of the following sentences have the same meaning?
1)I am concerned that she may think I stole the money.
I am concerned that she thinks I stole the money.
2)It is important that she may understand what her decision means.
It is important that she understands what her decision means.
The first pair do not mean the same thing: the second sentence expresses a definite fact in its first subclause – she really does think this; while the first subclause of the first sentence sets out a possibility, thanks to the use of ‘may’ – another way of putting it might be ‘I am concerned that maybe she thinks / she will think I stole the money’.
The second pair look as if they mean the same thing but in fact there is a slight difference, as much perhaps of tone as of meaning: ‘that she may’ implies that she should be given the opportunity to fully understand’ (leaving aside the ambiguous and opposing sense of this first sentence, along the lines of ‘she may understand what her decision means and we do not wish her to understand this, or because, if she understands this, then she understands other things which we do not wish her to understand, etc.’, a sense which could only occur in very contrived circumstances). The second sentence in this pair simply says that, from the speaker’s point of view and for whatever reason (e,g, for it to be a valid decision legally), it is necessary that she does indeed understand what her decision means, but
a) as pointed out earlier, it should be ‘It is important that she understand’ (subjunctive) and not ‘understands’ (indicative)
b) it does not imply, unless further qualification is added, that the speaker or the person addressed should take steps to make sure that she understands, unlike the first sentence.
(For completeness, I should note that this last sentence is in fact ambiguous, contrary to my earlier mistaken assertion: it could be taken in the same way as the first sentence in this pair, to mean that her understanding is important because we would prefer she did not understand the implications.)
Could I suggest that when you have to post further sample sentences in the same thread that you identify later ones e.g. as Example 2, Example 3, etc, so that people following the discussion can easily refer to the correct set of sample sentences ? Thanks.