Active duty military personnel are men and women currently in uniform and being paid. Retired military members are former active duty personnel. Here's another definition: Those the Pentagon can order to do something today are active and those the Pentagon used to be able to order to do something are retired.
Active duty personnel are in one of these branches of service: The Air Force, Army, Navy, Marine Corps and Coast Guard. They are under orders.
The retired military are men and women who used to serve in one of the branches of the service. They were under orders in the past.
There are also reserve units. These consist of former active duty military members on the path to full retirement plus part-timers. They have to make themselves available at the Pentagon's request, but they hold regular civilian jobs. They are potentially under orders.
National Guard units are run by the each state, not the federal government. They are also part-time units so sometimes they are under orders and sometimes they are not.
Active duty does not mean combat duty
Combat duty means working in an actual war zone. Active duty means being under orders potentially to be sent to a war zone as well as combat duty. Reserve and National Guard units can be called up to both active service and combat duty: Retired personnel are not called up.