In today's context, among Muslims, A jilbab(not to be mistook as jelabiya,which means dress) is a loose outer garment that starts from the head and goes all the way down to the feet. The abayah starts from the shoulder and may defer in fit and styles. The burkha I believe refers to the niqab, or face cover.
Now as to when people started wearing them, according to Islamic beliefs, it's been there for centuries. Different people wore different forms of these clothing and not always were they for religious reasons only. If you take the story of the Prophet Saleh(Peace be upon him) for example, you find even the women who disbelieved in his message wore face cover.
I also came across this video the other day on youtube from years ago that showed Christian ladies of noble standing participating in a funeral procession wearing what appeared to be very much like jilbabs and face covers too. Bare in mind I gave the above definitions according to us non Arab English speaking Muslims. Perhaps the Arabs may have contrasting definitions, Allahu alam.