Strictly speaking:
Bootstrapper:
A program that makes sure Windows Installer is installed. Originally intended to then call 1 MSI. But now the bootstrapper can call....
Chainer:
A program that handles the sequencing of various installers ( MSI or legacy )
MSI:
A database that describes the installation requirements of a product. Recent versions of MSI can chain other MSI's ( but not legacy packages ) but generally still require the use of a bootstrapper to make sure you have the most recent version of MSI.
Bootstrapper and Chainer are used somewhat interchangably. Some bootstrappers do all execution prior to invoking the MSI and some are more integrated with the MSI providing a robust UI and/or executing packages only if the MSI requires it for your situation.