A publishing site and a Team Site are common in many ways but there are some differences. Here I am going to talk about the High level differences without going Into too much of detail.
One of the main differences between a Publishing Site and a Team Site is that a publishing site can be customized to a larger extent than a Team Site. If you are planning to Install a 3rd Party tool like Akumina or Live Tiles, you could either deploy it on a publishing site or you could deploy it on the Team Site and activate the Publishing Features under Site Settings.
Some of the libraries that are available by default on a Team Site are not there on a Publishing Site. Some of them are News Feed and Calendars.
Finally, A Team Site is light weight whereas a Publishing Site requires more resources. So, while creating a new site you would need to think about the requirements and accordingly make a decision on which type of site you would need to create.