Answer:
Allocative efficiency is about distributing or allocating resources in the best possible manner. E.g. in order to fight the current pandemic, more resources ($) is allocated to different health care institutions.
Productive efficiency is about how a company or a person uses the resources that it has in order to produce the greatest amount of benefits at the lowest possible cost. E.g. in a hospital, if a doctor is able to treat 15 patients per day, his/her productive efficiency will be higher than another doctor that only treats 10 patients per day.