'Extend the offer' talks about giving an opportunity to someone, as seen in your example.
It can also refer to making the duration of an offer longer. For example, a shop might 'extend the offer' of half-price products for another week.
'Release the offer' is perhaps less commonly used. It might be used to talk about when the offer is first given, or first 'offered'.
Therefore, the two phrases are not exactly the same, but their meanings can overlap.