Joanne: start with previous means that the effects will both start at the same time.
start after means that after the effect before the selected effect is done entirely with what it's doing, the one after will start automatically.
Start with previous means that the animation will start at the same time as the previous animation in the order starts. Start after previous means that the animation will start immediately after the previous animation finishes.
Start timings… At the same time as, or after the previous one has finished.
Exactly what it says:
"start with previous" means it starts at the exact same time as the previous event – so the two will run at the same time.
"start after previous" means it doesn't start until the previous event has finished – so the first will run completely, then the second one will start.