Yes there are different sending elements associated with test sends versus live sendouts, especially in regards to authentication. On the contrary, if they specifically aren't receiving the emails, safelisting is the next step they should take to ensure their system isn't erroneously blocking the emails altogether.
If they're unable to resolve the issue from their side after safelisting your sending address and our domains, then I'd advise reaching out to our Delivery team for any further insight they may be able to provide regarding that particular contact (or their network).
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