I have had this conversation a few times lately so I wanted to take a few minutes and put together a quick blog post that helps define the two categories of site collections you can create in Office 365.
This category of site collection is your public website, your way to present your company data to an anonymous audience. This site collection is created one time for each tenant and is the only site collection that supports anonymous access. When you create this site you will see that it comes pre-configured with several common pages that would likely be present on a company’s public website.
This site is really pre-configured as a starting point for you to take and enhance with your own content. While this site is a SharePoint site, it is a special type of SharePoint site with a different subset of features. This means that you will work with this site differently than you will interact with Private Site Collections. For instance, instead of creating lists and adding web parts to this public site collection you will edit pages and add Gadgets. As you can see in the screenshot below, the interface is similar to a standard SharePoint site collection, but has some differences. If you are familiar with working on SharePoint sites you should be able to pick up on how to customize this public site very easily. Things will be a little different, but the changes should be obvious and easy to pick up on.
Private Site Collections
This category of site collection is where you are interacting and collaborating with others. Anyone who accesses these sites must do so with a username and password. No anonymous access can be configured for this category of site collections. If you are used to working with SharePoint on premise this is what you would expect when creating new site collections.
Each tenant can create multiple private site collections and then invite named users to access the created site collections. When you create the site collections you will be able to configure the properties for that particular site collection.