What is the proper term for a board that replaces a chip?
It would be called a 'daughter board' if it was intended (usually as part of the original design) to extend the functionality of the main board, eg. 

Amiga 1000 WCS Daughter board



A board which has similar chips to those it is replacing is commonly called a 'replacement module', particularly if it contains RAM.     

Example:-

ZX Spectrum 4116 (lower RAM) replacement module



If it uses eg. an MCU programed to replicate the functionality of a different type of chip it may be called an 'emulator'.

Example:-

SwinSID



A board with no parts on it for using chips or modules with a different pinout is called an 'adapter'. 

Example:-

Amiga 3000 SIMM ZIP Ram Adapter



As always there are overlaps and exceptions to these definitions. The word 'module' is often used to describe small boards with various generic functions (CPU module, RAM module etc.), so 'replacement module' could just be a module to replace another one.