Each time we generate a gmm model, we obtain slightly different clusters. Can we hence say gmm is stochastic? We obtain the same clusters if a random seed is set; does this mean given a random seed, gmm model is deterministic?
This is not directly related to Gaussian mixture models, but rather to how computers generate (pseudo) random data. Loosely speaking, there are two algorithms, one that generates a random seed, and a second that generates (pseudo) random data based on this seed. If you manually set the seed, the second algorithm always generates the same data. This what you actually see in your example.