I believe there is an analogy between the dual meaning of the word ”gene” and two senses of epigenetics, that this distinction is easy to get wrong and that it contributes to the confusion about the meaning of epigenetics. Gene can mean a sequence that has a name and a function, or it can mean a genetic variant. I sometimes, half-jokingly, call this genetics(1) and genetics(2). The order is wrong from a historical perspective, since the study of heritable variation predates the discovery of molecular genes. The first deals with the function of sequences and their products. The second deals with differences between individuals carrying different variants.
The same can be said about epigenetics. On one hand there is epigenetics(1), aiming to understand the normal function of certain molecular features, i.e. gene regulatory states that can be passed on through cell division. On the other hand, epigenetics(2) aims to explain individual variation between individuals that differ not in their DNA sequence but in other types of heritable states. And the recurring reader knows that I think that, since a lot of genetics(2) makes no assumptions about the molecular nature of the variation it studies, it will mostly work even if some of these states turn out to be epigenetic. In that sense, epigenetics(2) is a part of genetics.