The short answer is, no. The main difference is that press releases perform a marketing function for an organization, whereas a news release is about something that a journalist would decide is newsworthy or relevant. It could be about anything. For example, politics, crime or a general interest story.
As we have seen, the term press release originated in 1908 in a world where most news was printed. Since then things have changed. Whilst the term news release represents a more traditional approach to communication, in effect a one-way monologue where the media decide on the narrative. This two-way digital communications environment has in a lot of ways restricted the power that journalists had. The narrative might be initiated by them, but once published the story will take on a life of its own.