Business essentials comes with a 50GB mailbox size and does not provide access to the Office suite of apps. Business premium comes with a full suite of business applications including Word, Excel & Outlook.
As long as you are paying for an office 365 licence, shared mailboxes are free up to a maximum mailbox size of 50GB
“Office 365” refers to subscription plans that include access to Office applications plus other productivity services that are enabled over the Internet (cloud services), such as Lync web conferencing and Exchange Online hosted email for business, and additional online storage with OneDrive and Skype world minutes for home.
Internet access is required to install and activate all Office 365 plans and to manage your subscription account. Internet connectivity is also required to access Office 365 cloud productivity services, including email, conferencing, IT management, and other services. Many Office 365 plans also include the desktop version of Office, for example, Office 365 Small Business Premium and Office 365 Enterprise E3. One of the benefits of having the desktop version of Office applications is that you can work offline and have the confidence that the next time you connect to the Internet all your work will automatically sync, so you never have to worry about your documents being up to date.