retirement means you finished 20 years of active duty time or more or the equivilent and qualify for retirement benefits. completing your ADSO makes you a veteran. at that point you become mr/ms or dr.
Retired status is different. You are not discharged or de-commissioned, you are put on the retired roll. They actually can recall you to duty if they needed you (they would more likely call you and ask you if you were interested.)
What you are describing is discharge. If you are on IRR, you aren't discharged, only transferred. When you request de-commissioning, you truly become a civilian again. No title except "Dr."
Agreeing with others; the defining documentation is:
A). Do your ADSO (and perhaps a few additional years, but not enough to reach retirement threshold and nor receipt of benefits), resign and get out with no benefits nor retention of commission. You get a DD-214 which characterizes your service, and you're considered a veteran if certain basic criteria are met. You do not retain your officer title.
B). Meet the published requirements for retirement eligibility. Receive retirement orders (not a DD-214) and a blue retiree ID card (technically a form DD-2). Enjoy lifetime benefits, such as pension, base/post privileges, medical, pharmacy, etc. Retain officer commission in retired status. Still on the personnel rolls, can be involuntarily recalled to active duty.