Understanding how biological neural networks are shaped via local plasticity mechanisms can lead to energy-efficient and self-adaptive information processing systems, which promises to mitigate some of the current roadblocks in edge computing systems. While biology makes use of spikes to seamless use both spike timing and mean firing rate to modulate synaptic strength, most models focus on one of the two. In this work, we present a Hebbian local learning rule that models synaptic modification as a function of calcium traces tracking neuronal activity. We show how the rule reproduces results from spike time and spike rate protocols from neuroscientific studies. Moreover, we use the model to train spiking neural networks on MNIST digit recognition to show and explain what sort of mechanisms are needed to learn real-world patterns. We show how our model is sensitive to correlated spiking activity and how this enables it to modulate the learning rate of the network without altering the mean firing rate of the neurons nor the hyparameters of the learning rule. To the best of our knowledge, this is the first work that showcases how spike timing and rate can be complementary in their role of shaping the connectivity of spiking neural networks.