Andy Neil wrote:
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"Ok, you might say 'Assembler',..."

I absolutely would!

"but I see it as compiler, too ... sort of ..."

Absolutely not!

The tool which converts assembly-language source into object is called an Assembler;
The tool which converts high-level language (HLL) source (eg, 'C') into object is called a Compiler.

Assemblers and Compilers are two very different animals, and not to be confused; the terms are not interchangeable.
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Yes, Sir. :-)

I did not expect that the difference is so important to you. I hereby declare that I do not use any compilers, but only the two assemblers mentioned above.