In the VAEs Lab, before taking a dive right into the ELBO, some explanation of terminology is given. It would be great if someone can help me understand it in a better way. I have attached the specific part for reference.

Here, what’s the difference between p(z) and q(z)? Aren’t both representing the Multivariate Normal Distribution that is constructed by the outputs of the Encoder and taking samples from which, we pass on to the Decoder?

Additionally, how the 2 given mathematical notations are equivalent? Do explain that as well. Thanks in advance!