There are various tools that interact with Advanced Packaging Tool (APT) and allow you to install, remove and manage packages in Debian based Linux distributions. apt-get is one such command-line tool which is widely popular. Another popular tool is Aptitude with both GUI and command-line options.
If you have used apt-get commands, you might have come across a number of similar commands such as apt-cache, apt-config etc. And this is where the problem arises.
You see, these commands are way too low level and they have so many functionalities which are perhaps never used by an average Linux user. On the other hand, the most commonly used package management commands are scattered across apt-get, apt-cache and apt-config.
The apt commands have been introduced to solve this problem. apt consists some of the most widely used features from apt-get, apt-cache and apt-config leaving aside obscure and seldom used features.
With apt, you don’t have to fiddle your way from apt-get to apt-cache to apt-config. apt is more structured and provides you with necessary options needed to manage packages.
Bottom line: apt=most common used command options from apt-get, apt-cache and apt-config.
I have written in detail on the difference between apt and apt-get.