Why is Active Duty so called? My understanding is everyone on AD is Regular Army. So why not use the traditional name Regular Army?

All squares are rectangles, but not all rectangles are squares.

I think you misspoke when you said, "everyone on active duty is Regular Army" and meant it the other way around or said "is" when you meant "is not", as almost all individuals on full-time military service in the Army are on "active duty", but only a majority of them would be classified as "Regular Army" (full-time reserve component service members make up the lion's share of the rest).

You are correct in specificity (assuming you did mean it the other way around), but since most are never educated on the differences between those terms and the types of active and inactive duty, it's just 'one of those things'.

Why do most people often call generic things by a brand name (Jell-O, Band-Aid, Fiberglass, Super Glue, etc.)? Because that's how it was always referred to in their experience. Even when you point out that they are technically wrong, they usually fall into the "who cares? You know what I mean!" mindset.

In fact, it's so commonplace that even the U.S. Army refers to it as "Active Duty" when they mean "Regular Army" in the recruitment literature*. You, I and the majority of those reading these comments know the difference, but to the average civilian, they completely understand if you talk about enlisting on Active Duty, but are a bit confused if you talk about enlisting in the "Regular Army".
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* https://www.goarmy.com/explore-the-army/army-structure/active-duty.html

The term "Regular Army" is often not considered in its historical context.

It came into existence after the Continental Army was transformed from a volunteer force to a standing army. In theory the current U.S. Army is composed of 3 components: Active, Reserve, and National Guard.

To CSM Chuck Stafford's point, until the NDA of 1920, there was the possibility of holding Army rank in any component (or multiple) of the "The Army of the United States" (composed of the the United States Army, the Regular Army, the United States Army Reserve, the Army National Guard of the United States, the U.S. Volunteers, and the U.S. Veteran Reserve Corps).

As the other armed force branches became more defined and shortly before the Korean War, the United States Department of War became the Department of Defense, including the United States Armed Forces that houses the United States Department of the Army (+the other branch departments). In the DA there is the United States Army and its 3 components.

This is where is gets confusing, the Regular Army as a concept is short for "The Army of the United States" and is often confounded to mean "Active Duty", which would be technically incorrect (considering a given time period). However, "Regular Army" has been a stand-in for "Active Duty".

Active duty is full-time. Regular Army hints at the existence of an irregular Army...

In the old days, when we had Serial Numbers, they would be prefaced with RA or US and it mostly made a difference to the officers, I think. Not everyone on active duty was Regular Army. I think enlisted draftees were US. If you were recruited you were RA.

Historically, you can de called many thing. In the late 60'2 and 70.s you could VOLAR, and be AD or even drafted. The Title many decided how/which group was paying for you tring, meals etc. At the Mess hall line you had to announce AD or R, or Draftee. You can still be AD or USAR, ec.

I'm on ADOS orders, so I'm active duty but not regular army.

Activated reservists are not regular army but they are active duty.

AGRs are not Regular Army though they could be active duty for over 20 years in a row.

My understanding is retiree recalls are also not regular army.

It is much more useful to use verbiage like NG on Active Duty for several reasons - Pay, training, entitlements, etc.

Regular "insert here" is commonly used but it doesn't always mean the same thing which is why it isn't used to replace Active Duty. It all depends on context.

Regular Army can mean Active Duty
It also could be used to define a traditional deployable line unit in comparison to SOCOM units or other units that aren't "regular" like training command, Development Commands or other unique environments. We have similar situations in the Marine Corps. Deployable Infantry units are referred to victor units and deployable forces would be in the Fleet Marine Force, FMF or just Fleet. Which leaves alot of other units out there that don't fall into that cookie cutter like Embassy Guards, Recruiters, Development/Management units and many other unique opportunities out there.

I'm Active Duty now but not Regular Army. When I was in the Regular Army, I was USAR. Clear as mud. Lol.