In Office 365 when you create a new site collection, the Web Site Address gives you the option to choose to create your site collection under "sites" or "teams". What is the difference and why would you choose one over the other?
There is no real difference, it is a matter of taste and consistency,
I for example would create my projects and team sites under /teams, and other types of site collections under /sites
This blog seems to describe Managed Paths in an Office 365 context quite well: http://schakrabortytcs.blogspot.se/2011/10/office-365-sharepoint-online-managed.html?m=1
Robert is absolutely right. To summarize though there are 2 main types of managed paths, which practically control whether you go Wide vs. Deep in your URL structure (when creating site collections):
You must also be aware that it is recomanded to keep to < 20 per Web Application, so you need to balance carefully how new Managed Paths are created.