Earlier quoted context omitted.
Let us see... in my day, we called an "asm code generator" an assembler... anyone remember MasterSEKA, Devpac, TRASH'M-One and ASM-one?
1. Program that reads some input (e.g., C language) and generates asm and/or opcodes. 2. Program that reads asm and/or opcodes and generates binary numbers ("object files"). No. 1 is what I need. No. 2 is what I call an "assembler". Although terminology means less to me than what a program actually does.
So, back in the day (and still for me, always):
assembler: ASCII source code in assembler language -- "which language did you code that in? - Assembler."
assembler: the integrated development environment (such as ASM-One) which produces executable machine code straight from source, with no linking step in-between; also known as a two-pass optimizing assembler.