Practical difference between Bayesian Neural Networks and Feed Forward Neural Network with Gaussian Noise

Question

To my understanding, a BNN's weights come from a Gaussian with trained mean and standard deviation, while a FFNN of the following form, comes from a learned weight, which acts as a 'mean', and is multiplied by an untrainable standard deviation

Dense()
GaussianNoise(stddev=0.3) 

What is the practical difference between these two approaches?