Management-Buy-Out (MBO)

This is a term that comes up regularly following on from a business acquisition. What exactly does this mean and how does this differ from a management buy-in (MBI)?
An MBO is an acquisition of (part of) a company by the existing management and possibly other staff, either with outside financing other otherwise. An MBI is an acquisition of (part of) a company by one or more persons who will take over (a part of) the control of the company themselves after the acquisition.
The difference, therefore, is whether the company's buyer was already involved with the company prior to the acquisition.