In biology, when the presynaptic releases a neurotransmitter (a positive amount of them, obviously), this neurotransmitter reaches the postsynaptic vesicles causing an excitatory (depolarization) or inhibitory (hyperpolarization) effect, depending on the kind of postsynaptic vesicle in next cell dendrites. If the total amount of depolarization (all dendrites) is enough bigger than hyperpolarization, the neuron triggers an action potential or similar signal, continuing with the chain.
In the artificial NeuralNet parallelism, when the activation function of previous layer provides an output (say positive one) this value is multiplied by the weights of next layer cell. If the weight is positive, the effect is excitatory, if the weight is negative, the effect is inhibitory.
Thus, these two models are functionally equivalent (same excitatory/inhibitory target is covered), just make the analogy between kind of postsynaptic vesicle with the input weight sign of the artificial neuron.