You have discovered what so many of us have been pointing out for years: there is no delineated structure called "the foreskin". It's all just penile skin. No dotted line for doctors to cut along, which is why no 2 circumcisions in the world are alike.
Generally speaking, the penile skin that most physicians consider to be the foreskin runs forward from just below the (covered) corona of the glans. In practice, circumcision is not this neat because a certain amount of inner foreskin has to be left after a circumcision, so it can heal to the remaining shaft skin. But generally, what we call foreskin is about 50% of the infant penile shaft skin. (51% on average is removed in a neonatal circumcision, according to the 1996 Taylor study in the British Journal of Urology).
The foreskin can be thought of as having two primary components, the posthe and the acroposthion. The posthe is the part of the foreskin that is fused to the glans at birth and for a few years afterward. The acroposthion is the loose "snout" that hangs beyond the meatus of the penis. It may be tubelike, or resemble a spigot, or be almost nonexistent; there's variation. It is this acroposthion that was removed in ancient times, while the posthe was usually left, but modern "medical" IMC (infant male circumcision) removes both.
Because the foreskin is a double-layered sleeve, it can be retracted by "unfolding" the skin along the shaft. Retraction involves putting mild pulling pressure on the shaft skin or foreskin in the direction of the pubis, gradually eliminating the acroposthion and -- the worse part of premature retraction -- starting to reveal the glans. Some doctors retract gently only to the point of being able to view the urinary meatus to check for abnormalities or inflammation, while other doctors may try to retract a boy fully to expose the entire glans and even coronal sulcus. This is not recommended and could be damaging.
There is a naturally occurring condition called "aposthia", or being born without a foreskin (full or partial). It is rare and considered a birth defect.