They're not identical but they are related. There's a series of approximations and simplifications you can go through to get from biological neurons to neural n

They're not identical but they are related. There's a series of approximations and simplifications you can go through to get from biological neurons to neural nets. Essentially the weights in the neural net end up corresponding to steady-state firing rates of populations of spiking neurons. See for example Chapter 7 of Dayan & Abbott's Theoretical Neuroscience.