What is the difference between an Australian police check (National Police Check) and an Australian Federal Police check (AFP)?

Both check the same police records. Determine what you need a police check for as a first step. 

For immigration or visa purposes, or employment with the Commonwealth Government you must supply an Australian Federal Police check. Refer to our Australian Federal Police check page for further details. 

An Australian police check is acceptable for all other types of employment in industries such as education, health, banking and finance, and childcare.