The term "open return" is best avoided now.
This used to be the name of a ticket type (First Open Return and Standard Open Return) which existed until 2008, indeed this product still exists today, but is called an Anytime Return. The codes FOR and SOR remain in use. This ticket type used to indicate that there were no break of journey or time restrictions
On Track Retail booking sites use the term "open return" to mean "any ticket that is valid to return within one month" and won't return any results if the only return fares available are day returns. Tickets that prohibit break of journey or have time restrictions are included in these results.
Trainline booking sites use the term "open return" to mean "any ticket that is valid to return on more than one train", including returns that are only valid to return the same day, and returns that have hefty restrictions, which really casts doubts on whether the term "open" is appropriate in this context.
So, with no common definition of the term "open", it has effectively become a meaningless term, and when anyone uses that, you have to use context to attempt to figure out which of the above meanings they have in mind, or perhaps they have their own, completely different meaning in mind, who knows...!