I'm having a lot of trouble expressing my questions properly when I'm trying to ask other questions on this topic, so what is the proper name for a program running directly on the machine in question?
A term that could describe both a kernel, and a bootloader in the sense that they are being executed directly without an operating system?
The C standard calls that a "free standing environment", which strikes me as about as good a term to use as most others I've seen.
I would just use the term "standalone" because that's essentially what it's doing. Standing alone, without the benefit of an operating system.
Regardless of the term you use, you'll probably still find it useful to define it at least once in your question, then, once defined, you can use it to your heart's content.