For all I understand (and I understand little), dream productions is a part of dream entertainment. Dream productions manages the production stuff ofc and dream entertainment manages the artists. The beef is about who gets to be at the top of them though, hence the two sides about one favoring executive director yoon and the other full of people against the idea of him running dream productions. Since jay has a lot of dream productions' stocks, I think that is also the reason why that old fart wants him to sell his stocks so that dream productions can be his.
Someone correct me if I am wrong please lol
Dream Entertainment is the parental company that owns rights etc. Like Warner Bros. Dream Production is the production company that makes ie executes and produces the actual film. They may or may not be owned by the parental company or be an independent hire. Like Lionsgate Productions.
I have 0 idea what the difference between dream productions and dream entertainment is, nor do I know what the beef is between them.