Below are some points which will tell you the difference between these technologies:-
Talking about Docker CE, so it is the simple classical Docker Engine. Whereas Docker EE is Docker CE with certification on some systems and support by Docker Inc.
Docker CE is a free, open-source version of Docker. On the other hand, Docker EE is a paid version that one pays per node.
Docker CE which stands for Docker Community Edition is ideal for developers and small teams looking to get started with Docker. Whereas Docker EE or Docker Enterprise Edition is better for larger organizations which gives lots of servers they need to run; and, they need maybe management GUI. or LDAP authentication for active directory, or maybe they just need 24/7 phone support.
Docker is an awesome technology and if you do not know it then I would suggest you must learn it. If you want to learn Docker then you must take up the following Docker Training Course. Here is a video tutorial on Docker which you must watch to learn more about it.