I am watching the Sequence models course taught by Andrew Ng. I am a bit lost on the SimpleRNN lecture. As per the lecture, at each time step, there's an output y from a hidden layer and an input activation from the preceding layer. However, I do not understand what's the difference between the activation and output $y$ at any time step (except the first).
As per my understanding -
$$y = activation(w*x+b)$$
Therefore $y_t$ and $activation_t$ should be the same. I have included a figure to describe my issue.
In the picture, what's the difference between $\hat{a}^{\langle t \rangle}$ and $\hat{y}^{\langle t \rangle}$?
Here's the link of the lesson - https://www.coursera.org/learn/nlp-sequence-models/lecture/ftkzt/recurrent-neural-network-model