"Assembly" vs. "Assembler"
Actually, the language is called "Assembly Language", and the tool to convert it to machine code is the "Assembler".
More info on Wikipedia: http://en.wikipedia.org/wiki/Assembly_language
The purpose of language is to communicate.
If people say things, and other people understand them, they are using the correct terms.
We have rules to make it easier to understand, but in my opinion, if you say what sounds best for you, and let other people say what sounds best for them, and you all understand what you all mean, then everything will be peachy.
For what it's worth, I prefer to write "assembly" and assemble it with an "assembler." I think "assemblator" should be the word of the day someday, and everyone should try to use it as often as possible.