TLDR: On a personal level Efficiency is about staying at the PPF while Productivity is about extending the PPF.
I use to tell people how certain professions affect the Production Possibility Frontier.
(image from Investopedia)
Doctors try to keep output at a certain point along the PPF. This is because doctors try to keep you alive and healthy for as long as possible.
The fewer people there are the lower the PPF is.
Lawyers supposedly create transactions in a low trust environment. They allow people to operate at a certain efficiency. The creation of trust or trust substitutes by lawyers may also allow us to operate near the PPF.
Engineers like lawyers can allow us to operate near or at the PPF. Engineers also when they invent new processes allow us to extend the PPF.
Researchers/Inventors/Innovators more so than engineers allow us to extend the PPF. This can be illustrated by silicon technology. The science of transforming sand to silicon has made an abundant resource the foundation of what some people term as the 4th industrial revolution.
Giancarlo Angulo's Blog