Nope, Brave Rewards and Brave Wallet are two separate things. Brave wallet essentially works the same as MetaMask and alike, it's just already integrated in the browser.
Brave wallet seems to be an open source wallet.
Their source code on Github
https://github.com/brave/brave-browser/wiki/Brave-WalletBrave browser has bad history and broken their own slogan on privacy, by requiring their users to KYC for claiming BRAVE rewards from web browsing. I dislike that policy change from Brave browser and Brave wallet is developed by Brave browser team so I don't trust this wallet as well as the Brave browser.