I would imagine the word assembly refers to a model (family).
To my understanding, just like Assembler is a low-level language, basically the translation of functions into specific machine code (move data between registers, set flags, and perform machine-specific low-level functions). Every processor architecture (assembly) has its own flag, register, and instruction set... 8085, 8086, 8051, etc. all have their own assembler.
Programs written in higher level languages (like C++) have to be translated (assembled) into specific machine code in order to be executed...