MVPs are used to discover when a product is useful. MBIs are used to define the smallest increment of value that can be built and released that realizes value for the business. Although both of these are about doing a small amount of work and releasing it, they are quite different in both intent and method.
An MVP is intended to create a new product without an existing customer base. It is built by taking the smallest step possible to determine if it is viable. An MBI is for building the smallest enhancement to an existing product.
MVPs start out small. MBIs are generated from larger initiatives and are defined around market segments. They are defined by looking at initiatives and finding what smallest piece makes the most sense to release quickly.
MVPs are a sequence of small steps of discovery. MBIs are taking a large initiative and breaking it down into small pieces.
The release methods are also different. MVPs usually have a separate group building them and often don’t go through normal marketing or support channels. MBIs, however, are about product extension and must include normal marketing and support.
MVPs and MBIs are far from interchangeable concepts.