Website Scope
Each payment profile belongs to one Magento website. It is considered only when checkout runs on that website.
The profile form refreshes its payment-method choices when the website changes. Review the selected methods after changing website, because payment methods may be enabled or configured differently across websites.
For a multi-website store, create separate profiles with website-specific names and test each storefront independently. A profile from another website is ignored even when its customer group, priority and conditions would otherwise match.