What the old money headline established
In August 2021, AS reported a Madrid offer of €170 million plus €10 million in bonuses for Kylian Mbappé. That was reporting about a proposed transaction with PSG, not an official record of a completed €170 million transfer. A bid can be rejected, changed or expire without a signing.
Source [1]The later confirmed announcement
Real Madrid's June 3, 2024 official statement confirmed an agreement for Mbappé to become a Madrid player for five seasons. The short statement does not establish the old bid as the fee for that later move. Three years and different circumstances separate the two stories. Keep proposal amounts, salary estimates and confirmed contract terms in separate categories. The Lewandowski guide supplies a useful comparison because Barcelona explicitly published a base transfer amount and variables in its own announcement.
Source [2]