Do these two idioms mean the same thing or is there any difference between them? I'm just guessing, but maybe "Word is out." means that there is a rumor going around, while "The word is out." means that people are talking about a particular subject or they now know of a particular secret. Am I close?

Thank you in advance.
'The' is the pronoun of specificity or previous mention. The two sayings have the same meaning, but one would be preferred over the other depending on context (that is, whether the information which has been released is specifically stated or has been previously mentioned).
Thank you.