They may not be so similar actually- aside from the fins on modern models, there is a big difference in construction and mission.
No one expects a small-arms or gravity propelled flechette to penetrate armor, and no one really plans on using 120mm APFSDS rounds against a single person wearing body armor....
Flechettes also seem to be made pretty simply- a single piece of metal hammered into a sharp point with some integral fins.
Penetrators are optimized for material density with metals like tungsten or depleted uranium- but, only in the penetrator portion, which usually has a dull, rounded point, protected by a ballistic windshield with a very sharp point, made of a softer metal, that acts like a "shock absorber" to prevent the hard material of the penetrator itself from shattering on impact with armor.
Optimized design for hard-material defeat, compared to simple metal designs- maybe this, and the target intended is the defining point between the two.....
This falls back to the beginning of the thread and the thought of anti-personnel /material vs anti-armor, which I believe remains the most easily supported definition. I take exception to your point, however, that flechettes are somehow less engineered that AP rounds. If you jump to the Flechette thread, you may note that flechettes are not always simple wire with fins instead of a nail head.
When you compare Flechettes to AP rounds as "simple metal designs vs optimized design" you are ignoring decades of research and hundreds of specialized loadings, done by the US and many countries in Europe, not to mention the little we know about experiments and use in Russia and the Far East.
There have been flechetes with tracers, rocket assist, explosive loads and toxic loads. Loads for artillery, mortars, rockets, bombs, submunitions, shotguns, rifles and "special devices". Fin stabilized, fin/spin stabilized, mass stabilized - You even have current issue mixed loads with very large flechettes for building penetration mixed with very small for anti-personnel purposes (PAWS).
To categorize all flechettes as "a single piece of metal hammered into a sharp point with some integral fins" is akin to calling all APDS rounds a "hardened bullet with a fall-away sabot". Not much design work there.
I think that the two types of rounds are much more similar than most realize, they follow a very similar design train, with the primary difference being what has already been discussed, the target. Beware of over simplifying though, there have been a lot of unusual pieces out there, on big stuff as much as the little. Remember that "darts" were not limited to AP rounds. There was a 155mm discarding sabot experimented with, an 8-inch, and as I recall, for a period the US loaded 280mm projos into sabots for the 16-inch gun. While I don't think anyone would call these flechettes, it still brings you to the question - why not? Target remains the easiest answer.