They're different, but the terminology is often misused. I'll just link to and quote the relevant Wikipedia articles:
https://en.wikipedia.org/wiki/Deep_web_%28search%29
The Deep Web, Deep Net, Invisible Web, or Hidden Web are search terms referring to the content on the World Wide Web that is not indexed by standard search engines. Computer scientist Mike Bergman is credited with coining the term in 2000.
The first conflation of the terms came about in 2009 when the deep web search terminology was discussed alongside illegal activities taking place on the Freenet darknet.
Since then, the use in the Silk Road's media reporting, many people and media outlets, have taken to using Deep Web synonymously with the Dark Web or Darknet, a comparison Bright Planet rejects as inaccurate and consequently is an ongoing source of confusion. Wired reporters Kim Zetter and Andy Greenberg recommend the terms be used in distinct fashions.
https://en.wikipedia.org/wiki/Dark_Web
The Dark Web, also confusingly referred to as the Deep Web and conflated with Deep Web search is the World Wide Web content that exists on darknets, networks which overlay the public Internet and require specific software, configurations or authorization to access. The Dark Web forms part of the Deep Web, the part of the Web not indexed by search engines.
The darknets which constitute the Dark Web include small, friend-to-friend peer-to-peer networks, as well as large, popular networks like Freenet, I2P, and Tor, operated by public organizations and individuals. Users of the Dark Web refer to the regular web as the Clearnet due to its unencrypted nature. The Tor dark web may be referred to as Onionland, a reference to the network's name as "the onion router."
By these descriptions, arguably everyone in the cryptocurrency space is using the Dark Web and hence the Deep Web, since cryptocurrencies are P2P networks that "require specific software" to access. Also, (ahem) I'm assuming everyone involved in cryptocurrencies is using Tor (right?).