They are most certainly not twins. The kicks in Hapkido are almost exclusively circular and not related one bit to Taekwondo (old or new).
Really? What is your background in Hapkido? What system of Hapkido, specifically, did you train in?
I ask, because there are an awful lot of Hapkidoin who will disagree with you.
Here, as you can see, we have a low front kick (done with the side of the foot, which makes perfect sense for a sweeping type kick aimed at the lower leg), a mid-level front snap kick, a low side kick (I don't care for the super high chamber, personally), and a high inside crescent kick.
Continuing on, we have an outside crescent kick, a high roundhouse, a high front kick, an axe kick and a thrust kick.
All of these kicks (with minor differences - i.e. I wouldn't do the super high chamber on the side kick) are taught in TKD. And all of them are linear. In TKD, "linear" does not mean that movements are always in a straight line. It means that power directly opposes power. A crescent kick, although it is a non-linear movement, is still intended to apply power in a direct manner to the target.
The notion that "linear" means "straight movements" is common amoung new students. But do you think it's possible to do, for example, Kaunde An Palmok Makgi while moving the arm in a straight line? Even what could well be the simplest block in TKD, the low block, requires the fist to move in an arc.
TKD incorporates joint manipulation/throws from HK, but to a very basic level. For instance, we've covered four 15 minute classes/training in about 3-4 months of training, 3 days a week.
Blink and you miss it!
It's probably a mistake to extrapolate the entirety of TKD from your limited experience, don't you think?