Sorry, perhaps I wasn't clear. I was referring to an 'open' return (within one month). I've edited my original question to reflect this.
People are quite rightly confused, and it's not your fault, because the Rail industry used to use the term "Open" (yes, with a capital O!) to be a product of a ticket that had validity (on both portions) for one month, and was also valid on any train. However Thetrainline confused things by using the term "open" (note the lower case o!) to refer to a ticket that was not restricted to a particular train (but, in fact, may only have a validity of one day and may have restrictions - a far cry from an Open Return ticket!), and this terminology was then used by other booking websites.
Then we got "Simplification", where the Open Return became Anytime Return. No longer was the outward portion valid for a whole month (it was initially a day or two, then extended to 5 days) although the return portion remains valid for one month.
Now it is difficult to know what the term "open" means; does it mean any ticket that is not an Advance, including Day returns? Or does it mean a ticket that is valid on any train where the return portion is valid for a month (in some cases an Off Peak Return would count) Or does it mean something else? There is no common consensus as far as I can determine.
Therefore, my personal recommendation is to avoid using the term where possible. The rail industry has confused us all!