This work presents insights into the device physics and behaviors of ferroelectric based negative capacitance FinFETs (NC-FinFETs) by proposing lumped and distributed compact models for its simulation. NC-FinFET may have a floating metal between ferroelectric (FE) and the dielectric layers and the lumped charge model represents such a device. For a NC-FinFET without a floating metal, the distributed charge model should be used and at each point in the channel the ferroelectric layer will impact the local channel charge. This distributed effect has important implications on device characteristics as shown in this paper. The proposed compact models have been implemented in circuit simulators for exploring circuits based on NC-FinFET technology.