That's exactly right Dr. Dickie. Well except that an HBAR doesn't automatically mean it's accurate. It just means the barrel is stiffer than a thinner barrel of the same length. That is normally a good thing for accuracy, but there are lots of other variables in how that barrel is made.
Unfortunately Loxety, "regular AR15s" do all have HBARs these days. To get a lightweight barrel, you have to pretty much specially order it that way. Some M4 type carbines (which are supposed to have a lighter, thinner barrel under the handguards, see pic below) are HBARs with just a cut in front of the sight to make them only casually look like M4 profiles, very misleading.
Always ask the seller to remove the handguards so you may inspect the barrel thickness between the reciever and the front sight block.
Some common barrel profiles:
A1 profile: 20" Thin all the way (sometimes called a Pencil Barrel)
Superlight:
Pic Here. A 16" barrel same as above.
A2 Government profile:
Pic Here.Thin under the handguards, thicker in front of the sight. Usually 20", some 16" Midlengths are made this way.
M4:
Pic Here. 16" Thin under the handguard, thicker in front of the sight, but has a groove cut there (to mount the front of the M203 grenade launcher on the military guns). this profile is sometimes seen on Bushmaster Dissipator barrels.
M4 SOCOM: 16" Heavier under the handguards, but has a groove under there aslo, to mount the rear of the M203.
Then there's the HBAR.
Pic of a 16",
pic of a 20"