(edit: Either confusion isn't a real problem, or else the confusion is inevitable and some new term will become the politically charged one with lots of contested meanings. In either case, the correct solution from your perspective should be more statistics education for more people rather than trying to change terminology.)
> All I said is that we should name it something else
As I said elsewhere, some mathematician would come up with a concept, name it after that new thing, and then we're back here all over again because "bias" is inherently moral and political and has shades of meaning informed by moral and political opinion.
You won't have solved the precision problem, or even the overloaded terms problem.
> Specifically, I think the term "bias" is used to make people think machines are drawing incorrect conclusions.. I think this will mislead people
I agree "bias" is a politically powerful word.
I don't agree, however, that people fail to know and understand the difference between (1) and (2).
And I also think all people know that the term "bias" could mean both, and manage to communicate with one another using the full range of their vocabulary whenever it's unclear what's being discussed. See e.g. internet discussions around stop and frisk or WoD or racial profiling at airports.
People understand the difference between (1) and (2), even when bias is used to refer to both.
I might be wrong about that. A far more important prediction: I don't think there's anyone -- on either side of the debate -- whose position can be explained by their misunderstanding of the statistical meaning of "bias".
People understand the statistical meaning (or not), and call (2) bias regardless. Because they aren't referring to a mathematical object, they're referring to the effect something has within a larger social and political context. A context that cannot be perfectly modeled, and so is necessarily vague and difficult to pin down.
The fact that "bias" can have both meanings isn't a real problem. People are good communicators and, when they want, can easily distinguish between (1) and (2).
Saying that (2) is "not bias" is definitely a political statement when taking the common definition of bias. People are free to agree or disagree with that statement, but arguing via way of naming clash isn't a compelling argument (not saying you're making that argument, but GP is I think).
> Why do you want to conflate these two situations?
I don't think this is a real problem.