There is no difference in the blessings: it is the same blessing, the same water. They are the same prayers each time. It is theoretically unnecessary to save two bottles, one morning and one night, except if you really want/need that quantity of holy water.
I have a feeling that the reason why there are two blessings is because there are two liturgies: one a Vesperal Liturgy, and one a Morning Liturgy. Theophany is one of the 3 days of the year that the Church will celebrate two liturgies on the same Liturgical day: Christmas, Theophany, and Pascha (Easter). Each of these days at some point were days of vigil, with the services beginning the evening before the feast and progressing into the morning of the feast (in monasteries they still are). Out of this grew the practice of evening and morning liturgies. The blessing of the water is to be done after Liturgy (when it was a vigil, then there was only one Liturgy - in the morning) as part of the celebration of the feastday. Now, since we do two Liturgies (unless Christmas or Theophany fall on a Sunday or Monday), the blessing was added before the evening service, since for many that will be their only celebration of the feast.
I hope this is helpful.