Should an app and a protocol be named the same or different things?

Uniswap is the app (website and now mobile app) and a protocol. This hasn't stopped developers from building on the Uniswap protocol.

In addition, in the previous cycle, many consumers wanting to trade tokens onchain used the Uniswap website. Others used wallets with swap functionality built on the permisionless Uniswap protocol.

For NFTs, the app and protocol were split—OpenSea and Seaport. However, since it was a consumer app, the brand being the thing consumers heard about meant that OpenSea was easier to find and onboard to. No one except for developers knew about Seaport. (Fair to say Seaport is less important protocol than Uniswap.)

Email and the web both have strong protocol branding that's independent of the clients. Same goes for Ethereum, and a lesser degree Solana (in the case of wallets).