Usually, every statistical model is a special case of a probabilistic model in which its parameters have been estimated by data. The regression E[Y|X] is basic

Usually, every statistical model is a special case of a probabilistic model in which its parameters have been estimated by data. The regression E[Y|X] is basically the mean of a gaussian distribution of Y given X with sigma set to the error term. The whole gaussian distribution part is the probabilistic model. But to estimate wich parameters make up this model in a particular application (together with how to check if it is valid or not) is the statistical modeling part.