RBMs have a native probabilistic output (the output is a distribution you can slice), but vanilla neural networks don't (the output is a vector). Is that right?
It's best to say that an RBM is an undirected NN which models a probability distribution of some variables. You can sample from the distribution (which is a stochastic process). There are other NN models which use feed-forward NNs to do similarly --such as GANs and VAEs and others. The generation process is also stochastic, but the difference is that you sample a noise distribution and then feed that through the NN. In all cases the generated samples are still vectors.