I hosted wallet would be a a wallet that I access through a virtual currency exchange (which FinCEN defines as an MSB). One of the most commonly used virtual currency exchanges is Coinbase.
An unhosted wallet would be an encrypted wallet that I install on my laptop, flash drive, mobile phone, etc. that is not connected to an exchange.
Unless your institution is offering hosted wallets as a service to your customers, this rule won't impact you at all. The OCC issued comments on national banks providing hosted wallets as an option. I don't have any of my clients that do.
https://www.occ.gov/news-issuances/news-releases/2020/nr-occ-2020-125.html
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