Diversity-multiplexing trade-off has been studied extensively to quantify the benefits of different relaying strategies in terms of error and rate performance. However, even in the case of a single half-duplex relay, which seems fully characterized, implications are not clear. When all channels in the system are assumed to be independent and identically fading, a fixed schedule where the relay listens half of the total duration for communication and transmits the second half combined with quantize-map-and-forward relaying (static QMF) is known to achieve the full-duplex performance . However, when there is no direct link between the source and the destination, a dynamic decode-and-forward (DDF) strategy is needed . It is not clear which one of these two conclusions would carry to a less idealized setup, where the direct link can be neither as strong as the other links nor fully non-existent. In this paper, we provide a generalized diversity-multiplexing trade-off for the half-duplex relay channel which accounts for different channel strengths and recovers the two earlier results as two special cases. We show that these two strategies are sufficient to achieve the diversity-multiplexing trade-off across all channel configurations, by characterizing the best achievable trade-off when channel state information (CSI) is only available at the receivers (CSIR). However, for general relay networks we show that a generalization of these two schemes through a dynamic QMF strategy is needed to achieve optimal performance.