Original answer (source u/friendlykitten123):
Auto associative Neural networks are the types of neural networks whose input and output vectors are identical. These are special kinds of neural networks that are used to simulate and explore the associative process.
And Autoencoders are an unsupervised learning technique in which we leverage neural networks for the task of representation learning.
The difference being is that Autoencoders need at least 1 hidden layer to be constructed. But, Autoassociative neural networks could be obtained through a bidirectional associative memory, which is implemented with no hidden layer, and whose weights are learned in one step.
For more information, you can visit the following article:
https://ml-concepts.com/2022/03/10/everything-about-autoencoders/