8:10 AM PT -- While Christina Haack clearly thought Josh Hall was making a reference to her and their ongoing divorce, we now know that's not the case ... 'cause he was getting at something else entirely.

Sources with direct knowledge tell TMZ ... Josh was actually visiting a cop friend of his, who's terminally ill -- and he's being treated at a cancer treatment facility called City of Hope. Our sources say Josh dropped the blue heart to show solidarity with law enforcement.

In other words, this had nothing to do with Christina -- even though she clearly took it that way.

Christina Haack says her husband's recent Instagram post about hope's really all about cash ... claiming he's only hoping for even more millions than she's offered in the divorce settlement.

The reality home makeover expert took to social media to mock her soon-to-be ex-husband after he posted a huge sculpture spelling out "HOPE" ... seemingly saying he's holding on to his amid the bitter divorce proceedings.

Haack's taking a more cynical approach to the post though ... sharing the photo again, with her added "I 'HOPE' she pays me millions more than what she's already offered me."

So, in CH's comment, all Hall's hoping for is a payday ... despite what she seems to be saying is millions already on the table -- more money drama in a split already rife with it.

Remember ... Christina and Josh split last month, but they claim different dates of separation -- with Haack saying July 7 and Hall claiming July 8. Part of the reason for this, according to Christina, has to do with a $35k transfer from her rental property that went to Hall's account on the 8th.

Christina wants the money back. However, a source close to Josh says he only took the money to pay bills ... claiming he's still running the rental property despite their estrangement.

Haack and Hall married back in late 2021 ... her third marriage after previous couplings with Tarek El Moussa and Ant Anstead. She shares two kids with Tarek.

Seems too much to "hope" this divorce will be amicable.