Sim rate does affect the passage of time, even on full live mode. Stutters also affect the passage of time. When the sim still had terrible memory leaks I noticed the time falling behind the more the sim was stuttering.
Pause doesn’t stop time, time keeps going at the current sim rate, but the time can fall behind from stutters. Maybe going into the control bindings menu actually stops things. Just pressing esc keeps things going.
Sim rate affects the speed of your plane and fauna. But doesn’t affect the speed of weather, nor car traffic and AI planes. Sim rate also skips simulation steps rather than perform them at a faster rate, hence the dolphening effect on AP at high sim rate.
Which adds another question, what should a replay feature do when sim rate is used.