Perhaps she meant unscheduled cesearean, rather than emergency? I know
most people probably use those two terms interchangably, although
technically speaking it's not correct. I think that to most women, when
they've been laboring and dilating for hours and hours and hours, and then
mid-process the vaginal birth gets converted to a cesearean birth, most
women would label that an emergency c-section.

though again, you could argue that this is emergency c-section, if
progression is truely not occuring, and baby is not coming out vaginally
then at some point it is going to become an ermegency. I've heard the term
crash c-section, which seems to be when it really is an emergency, thus
distinguishing it from emergency as in, it's happening soonish because the
women is in labour. It's also terms used in hospital scheduling, operating
theatres tend to have an elective list and depending on the size of the
hospital a theatre dedicated to emergencies, or slotting them into the same
theatre, so emergency again might not mean needs to be done now. In the
hospital that was local to me in the UK, for an emergency that wasn't dire
you could easily wait 3 days to be slotted in, being nil by mouth until 10pm
each day when they confirmed they weren't going to do you that day!

Cheers

Anne