If I were to resume in a single phrase the difference between messianic time and apocalyptic time, I would say that the messianic is not the end of time but the time of the end. What is messianic is not the end of time but the relation of every moment, every kairos, to the end of time and to eternity.
[…] In the Judaic tradition there is a distinction between two times and two worlds: the olam hazzeh, the time stretching from the creation of the world to its end, and the olam habba, the time that begins after the end of time. Both terms are present, in their Greek translations, in Paul’s Letters. Messianic time, however – the time in which the apostle lives and the only one that interests him – is neither that of the olam hazzeh nor that of the olam habba. It is, instead, the time between those two times, when time is divided by the messianic event (which is for Paul the Resurrection).
… what is at issue is a time that pulses and moves within chronological time, that transforms chronological time from within. On the one hand it is the time that time takes to end. But on the other hand it is the time that remains, the time which we need to end time, to confront our customary image of time and to liberate ourselves from it. In the one case, the time in which we believe we live separates us from what we are and transforms us into powerless spectators of our own lives. In the other case, however, the time of the messiah is the time that we ourselves are, the dynamic time where, for the first time, we grasp time, we grasp the time that is ours, grasp that we are nothing but that time. This time is not some other time located in an improbably present or future time. On the contrary, it is the only real time, the only time we will ever have.
Agamben, The Church and the Kingdom