Tun/tap interfaces are software-only interfaces, meaning that they exist only in the kernel and, unlike regular network interfaces, they have no physical hardware component (and so there's no physical "wire" connected to them). You can think of a tun/tap interface as a regular network interface that, when the kernel decides that the moment has come to send data "on the wire", instead sends data to some userspace program that is attached to the interface.
On the other hand Virtual Machine Interface ("VMI") may refer to a communication protocol for running parallel programs on a distributed memory ststem.