I've heard these terms used interchangeably.
I think there are two situations where there are substantive, non-semantic distinctions between the two. The first is if the campaign in question is meant to shift people between products versus reaching a lapsed user for just one product.
For instance, if I operate a product portfolio with two products, A and B, and I know that users in Product A tend to also be very engaged in Product B, I might run a re-targeting campaign for Product B aimed at Product A users. The idea of re-engagement here wouldn't make sense since the users targeted in the campaign for Product B may not have ever been exposed to it.
The second potential difference is when re-engagement is used not for lapsed users but for engaged users to bring them into a specific "moment" in the product, like a sale or a tournament. You can imagine a mobile commerce app running a "re-engagement" campaign against its most active users around Christmas, and the term "re-targeting" wouldn't make sense for that since re-targeting is generally thought of as a means of re-activating lapsed users.