Hi Deborah.....I saw you message posted on this web site and hope I can help you. I don't know what records you have from your father but you can request his service records from the following web site: www.archives.gov this page will tell you how to go about getting his records. one thing you will need is the "standard form 180" and you can find it on this page. looking at the dates you posted I wonder if your father enlisted in the army on 8/15/41 and went oversea on 8/23/43? Active duty always meant when you were in service full time. Reserve duty I believe would be perhaps the "national guard". If the national guard gets called up or"activated" then that becomes active duty.Inactive duty I believe was used by some persons like doctors or professional people that wanted to keep their rank and would be called back to service in time of war.
Regular Army, when I was in, meant those who had enlisted. enlisted men always had a different type serial number and had RA in front of the number. you also have a three year gap between 12/29/45 and 12/22/48. was he still in the service for those years. I don't know if any of this helps but if you need any more help you may want to contact me on my e-mail address.
I also just noticed that you name is "Burke". It just so happens that my mothers maiden name was Burke from Connecticut and Brooklyn, New York.