Microsoft made some significant changes in SharePoint 2013 to reduce confusion and streamline the product. Creating a new site is a perfect example. Where you could create a site multiple ways in SharePoint 2010, there is now one way in SharePoint 2013.
You create a new site in SharePoint by doing the following:
Click the Settings gear icon and select Site Contents.
Click the New Subsite link, to open the New SharePoint Site form.
In the Title and Description text boxes, type a name and description for the new site.
Enter a unique site name that will be used in the URL in the URL Name text box.
Select the Team Site template for the site by clicking the Team Site template on the Collaboration tab to select it.
Notice that Team Site is not the only template option. You can choose other templates. Regardless of the template you start with, you can then develop the site to add SharePoint functionality as you see fit.
Choose whether to use the same permissions as the parent site or use unique permissions by selecting the appropriate radio button.
Choose whether you want to display this site on the top link navigation of the parent site or not by selecting the Yes or No radio button.
The top link navigation is the menu across the top of the site.
Choose whether to display the same top link navigation as the parent site or not by selecting the Yes or No radio button.
Click Create to create the site.
The new site is displayed in the browser.
Every SharePoint site is contained within another SharePoint site in a hierarchy. At the top of the hierarchy is a special type of site called a Site Collection. Creating and administering a Site Collection takes special permissions. Every site within the Site Collection is called a Subsite.
The site you just created is a Subsite of whatever site you were in when you created it. There are really no differences between using a site that is a Site Collection and a site that is a Subsite. To users, both types of sites look and act the same. The differences lie in the navigation, security settings, and features.