What do 'Invoiced' and 'Messaged' statuses mean?

There are 4 status possibilities:

'Messaged' means your shopper was messaged by the app after they commented and was asked about the variant option (if one exists for your product).

'Invoiced' means your shopper got a checkout link to purchase.They may not make it this far if they did not choose the variant options in the first message they received in the "Messaged" status.

'Bought' and 'Waitlisted' are self-explanatory (you can read about how waitlists work here)

There is a 5th possible status called "Error" which happens when the shopper's privacy settings prevent your page from contacting them in Messenger or when your page tries to message itself

In these cases, inventory is not adjusted since the user wasn't able to get a proper invoice.