RNNs are feedforward networks with shared weights

RNNs are feedforward neural networks with shared weights (and, usually, residual connections).

Feedforward vs recurrent: Unrolling an RNN in time results in a feedforward network with weight sharing and vice versa.
Layers vs iterations: A deep network with weight sharing is doing the same computation $L$ times.

See NODE, ResNet (discretized continuous-time dynamical system), dynamical-systems lens on neural networks