When is a conference charged?

[SAump]

OP: A game I was at, the defense called time, came out and made a pitching change. No charged conference for changing the pitcher.

"The pitching change was not a conference."
Here is another one.
"1. HC has conference with pitcher, and replaces him. No conference charged."

I am missing something here. I read it several times in this thread posted by several very knowledgable individuals. What am I missing?

New inning, new pitcher, no conference. Same inning, conference w/ pitcher and catcher, pitcher replaced w/a new pitcher, conference with pitcher and catcher, resume game. This pitching change is not a conference?