In the first instance, we have no control over the situation so 'hoping' seems natural. In the second, sometimes we might have an input, eg, if the hope is for good results in an exam, then how much revision was done is a key factor, which would mean that hope alone would be a somewhat 'vain hope'.
In the case of a health test perhaps, in some cases, no action of ours would have any impact so hope is a natural response, whereas there can be situations where our life-styles have an effect on results so maybe hope plus effort is to be 'hoped for.''
In the religious context, however, it is given a very high importance. Faith, hope and charity are, after all, entitled 'the three key gifts of grace' or theological virtues, to give them their more formal title.
Perhaps it is because I have always had absolute conviction that, whether in this life or the next, "All will be well," that I don't seem to worry about the ultimate future because there seems no need.
This might sound complacent but I don't mean it to be. I believe we all have to try as hard as we can to be good people in whatever circumstances life places us but, on the whole, I live fairly happily in the present, with my life, if not always with myself. And as for that, I have complete trust that, in the end God will sort me out and take me home.