Deep web and Dark Web are two different things, but as noted on Wikipedia the terms are often used interchangeably and incorrectly particularly by mainstream media.

The Deep web in simple terms is "anything on the internet that's not indexed (or index-able) by mainstream search engines". For example, the "internal" web pages you see after logging into internet banking or netflix etc.

The Dark web is websites that are only accessible via an overlay network running on to of the internet, the most common of which would be the Tor/Onion network. It's most often associated with "very" illegal things in the public eye (kiddie porn, terrorism, drugs, etc) but in general is just used for anonymity. Tor for instance was originally built with ONR/DARPA money to allow US spys to anonymously/untraceably communicate on the internet.