Autoencoder is a simple 3-layer neural network where output units are directly connected back to input units. Typically, the number of hidden units is much less than the number of visible ones. The task of training is to minimize an error or reconstruction, i.e. find the most efficient compact representation for input data.
RBM shares a similar idea, but it uses stochastic units with particular distribution instead of deterministic distribution. The task of training is to find out how these two sets of variables are actually connected to each other.
One aspect that distinguishes RBM from other autoencoders is that it has two biases. The hidden bias helps the RBM produce the activations on the forward pass, while The visible layer’s biases help the RBM learn the reconstructions on the backward pass.
