I subscribe to what I call the “clouded mirror” model. What gets communicated by me and the players at the table is reflected in what gets communicated and perceived by the characters in the world, but the mirror is cloudy. It’s not a one-to-one reproduction, just an approximation. I think most groups do this to some extent - for example, theoretically the characters are speaking “common,” not whatever language he players are speaking in. This extends to things like game mechanics as well. I say “DC 15,” not because your character knows the precise odds of success at a task, but because your character probably has a good idea how hard the task will be, and telling you the DC approximates that knowledge more closely and with less room for misunderstanding than a purely narrative description would.