There is a distinction. Dark web is usually associated with the Tor network. Deep web is stuff you can't access normally, like your email or someones Onlyfans.
The dark web is the World Wide Web content that exists on darknets: overlay networks that use the Internet but require specific software, configurations, or authorization to access.
Think of dark web as the high-security installations where the best Pokémon are found. And the deep web as all the hard-to-access parts of the world (like the Himalayas) that have been less exploited by Pokémon hunters so there's a better chance of getting rare-but-popular ones.