Not entirely the same thing. VAEs offer approximate likelihood estimation, but not exact. The difference here is key - VAEs do not optimize the log-likelihood directly but they do so through the evidence lower bound, an approximation. Flow based methods are exact methods - we go from an easy tractable distribution to a more complex one, guaranteeing at each level that the learned distribution is actually a legit distribution through the change of variables theorem.

Of course, the both (try) to learn some probability distribution of the training data, and that is how they would differ from GAN approaches that do not directly learn a probability distribution.

For more insight you might want to look at https://openreview.net/pdf?id=HklKEUUY_E