I definitely understand the difference, but what you may be misunderstanding is that at least in the case of a local union executive board. They get to determine if it’s an LBFO. Regardless of what the company says, and I’m assuming the international can do the same.
“The Local Union Executive Board shall determine whether an employer has made a final offer of settlement, regardless of the employer’s characterization. When the Local Union Executive Board has determined that an offer is “final”, such offer must be submitted to the involved membership for a secret ballot vote”