No, the dark web is not the same thing as the deep web. Picture the internet with three layers. The top layer is sometimes called the surface web, visible web or indexable web. This is the part of the web which most users are familiar with. It can be accessed by standard web search engines such as Google and Bing. The deep web is the second layer and this is where 90% of the information is stored.
Examples of data stored here include academic, medical, financial, and legal records. Encryption software with passwords is used to access the deep web. The dark web is the third layer; it is only accessible via certain specific web browsers/technologies and it contains a lot of illegal information such as where to buy weapons, drugs, and pornography.
The Deep web and the dark web are totally different from each other. The Deep web is simply referred to all the data that exists behind the firewalls. These include the web-archives, the websites that are protected by passwords, the user databases, and so on. It is said that the deep web is 400-500 times larger as the surface internet.
The dark web on the other hand, contains some anonymous websites that are present as part of the deep web. Since the dark web allows anonymity, it is full of illegal marketplaces for weapons and various drugs that cannot be obtained legally.