Excitatory-to-inhibitory cortical synapses exhibit either short-term facilitation or depression, depending on the subtype identity of the postsynaptic interneuron, while the short-term plasticity (STP) of inhibitory-to-excitatory synapses depends on the presynaptic interneuron. However, the rules governing STP of inhibitory-to-inhibitory synapses have not yet been determined. We recorded 109 unitary connections made by the two major inhibitory interneuron subtypes in layer 4 of mouse somatosensory cortex, fast-spiking (FS) and somatostatin-containing (SOM) interneurons, on each other and on excitatory, regular-spiking (RS) neurons. In all pairs, we measured dynamic changes in the postsynaptic response to a 20 Hz train of presynaptic action potentials. In half of our dataset, we also measured kinetic properties of the unitary IPSC: latency, rise time, and decay time constant. We found a pronounced dependency of STP on the presynaptic, but not the postsynaptic, identity: FS interneurons made strongly depressing connections on FS, SOM, and RS targets, while in synapses made by SOM interneurons on FS and RS targets, weak early depression was followed by weak late facilitation. IPSC latency and rise time were also strongly dependent on the presynaptic interneuron subtype, being 1.5-2× slower in output synapses of SOM compared with FS interneurons. In contrast, the IPSC decay time constant depended only on the postsynaptic class, with 1.5× slower decay on excitatory compared with inhibitory targets. The properties of the inhibitory outputs of FS and SOM interneurons reciprocate the properties of their excitatory inputs and imply a dynamic spatiotemporal division of labor between these two major inhibitory subsystems.