At first glance, the Lognormal, Weibull, and Gamma distributions distributions look quite similar to each other. Selecting between the three models is “quite difficult” (Siswadi & Quesenberry) and the problem of testing which distribution is the best fit for data has been studied by a multitude of researchers.
Despite their similarities, there are some subtle differences between the Lognormal, Weibull, and Gamma distributions. This one picture outlines the differences between the three models.
Gamma Distribution image: CBurnett|Wikimedia Commons
Lognormal image: Krishnavedala|Wikimedia Commons