I never really reason the two words having a different meaning but as I look up the words for online just now I come dey understand the difference although both words dey very similar and both has to do with withholding information from people.
From within I read, privacy na say you decided to hold the information for yourself while secret na say you no want make people know about the thing. So if you don't want people to know about your Bitcoin holdings na secret you dey keep so and this might involve you not telling your family because you no trust them.
But in the context of Bitcoin, I think both words can be used and doesn't have any difference because when you hold the information from your family, you're keeping your privacy and being Secretive at the same thing.
Even though the word really mean almost same thing for bitcoin space ba, OP seriously explained how seed phrase should be treated interms of our relationship, I think for family members most especially immediate ones like parents for single ones and wives or children for someone who wants to have family, you might decide to have to use both. Like you will tell your parents it’s a private thing and you want them to keep it as a secret, Same thing with your wife too.
The reason why you have to specifically tell them that it is a secret is because they might decide to have it private and extend the information to other family members most especially in a Nigerian extended family because they feel those people are in the bracket of private too, but telling them it’s a secret between you too is to simply safeguard the information between you two and your own way of telling them that it shouldn’t be voiced out to even immediate family members to them, as you want total secrecy