Phase change memory (PCM) is being actively explored for in-memory computing and neuromorphic systems. The ability of a PCM device to store a continuum of resistance values can be exploited to realize arithmetic operations such as matrix-vector multiplications or to realize the synaptic efficacy in neural networks. However, the resistance variations arising from structural relaxation, 1/f noise, and changes in ambient temperature pose a key challenge. The recently proposed projected PCM concept helps to mitigate these resistance variations by decoupling the physical mechanism of resistance storage from the information-retrieval process. Even though the device concept has been proven successfully, a comprehensive understanding of the device behavior is still lacking. Here, we develop a device model that captures two key attributes, namely, resistance drift and the state dependence of resistance. The former refers to the temporal evolution of resistance, while the latter refers to the dependence of the device resistance on the phase configuration of the phase change material. The study provides significant insights into the role of interfacial resistance in these devices. The model is experimentally validated on projected PCM devices based on antimony and a metal nitride fabricated in a lateral device geometry and is also used to provide guidelines for material selection and device engineering.