@Mr.Wizard There are two kinds of precendence. One that the kernel uses to create boxes, and one that the front end uses to parse boxes. The first question deals with the kernel, and the second seems to deal with the front end. So, I think it makes sense to keep them separate. Probably the questions could be clarified to point out this difference, though. I didn't bother because I felt that one of the answerers on the second question was ignoring my comments.

@CarlWoll I see. Please edit your question to clarify this as you mention as the subtlety was lost on me. Where do the two directions differ? I would have hoped they were consistent.

@Mr.Wizard The precedence table in the code parser that WRI has released on GitHub contains comments which detail discrepancies between the kernel parser and Precedence.