At my Taekwondo school, we practice the traditional hyungs as created by General Choi. After reviewing several materials for WTF practitioners and reading books on the history of Taekwondo, I'm left wondering what are the primary differences between the ITF-style hyungs and the WTF poomsae are. Specifically, is one more kick intensive? Stance intensive? What are the key characteristics that differentiate the two styles of pattern (if any!)?
Basically: The Hyungs are chaotic, the Poomsae are well-organized and (mostly) symmetric. Whether this point is in favor of Hyung or Poomsae depends on personal taste, I guess.
The Poomsae have a much smaller technical repertoire, especially, but not only, when it comes to kicks. (Palgwe: Front, Side and Crescent Kick; Taegeuk: Front, Side, Crescent, Roundhouse and Jumping Front Kick; Black Belt Forms: Front, Side, Crescent, Jump-Spinning-Crescent, Jumping Side Kick. This is ridiculously little for an art that claims to be the kicking art)
Personally, I have always wondered how a fascinating art like Taekwondo could come up with a forms system as boring as Poomsae (I hold a 5th Dan WTF, so I know what I am talking about).
At least the newer Poomsae school, Taegeuk, which replaced the older Palgwe school, was also designed to look less like Karate. Large parts of both Hyungs and Palgwe were copied from Shotokan Karate Kata, and that was an aspect the officials liked to hide (after all, TKD was "officially" 2000 years old and had nothing to do with Karate).
If you mean from a grammatical perspective, they are the same. They are synonymous.
But if you mean from a style POV, it depends on what you mean, so some clarification is needed. Typically, Kukkiwon universally refers to their forms as "poomsae", so when Taekwondo-in hear this, they almost always assume you're referring to Kukkiwon's poomsae. ITF is a little different. There are two branches of thought. One branch is more modern, and refer to their forms as "hyung". The other branch is older and more traditional, and refer to their forms as "tul" (a derivative of the Chinese word "taolu" which means... forms/hyung/poomsae/kata).
Those who refer to their forms as "tul" are almost always ITF-based, and usually perform their forms with a sinewave (up/down motion with each movement). Their kicks are generally very low, lending to the implication for self-defense. Likewise, their stances are moderate compared to Kukkiwon whose stances are very narrow and short, vs many ITF schools - particularly the "hyung" crowd - whose stances can (but not always) be very long and wide (a feature some say was adapted from Shotokan Karate).
Those who refer to their forms as "hyung" can be either modern ITF, kwan-based (that is, while officially belonging to Kukkiwon, they retain their original style look/feel), or traditional Tang Soo Do stylists. They can also be part of other Korean martial arts - like Hwa Rang Do.
Because of the wide variety of styles (modern ITF, kwan-based, tang soo do) who practice "hyung", it's not feasible to discern the differences, since each school will inevitably vary.
So I'll give my opinion on my form stereotype.
Bounce / sinewave: If you see someone "bouncing up a down with a deliberate emphasis on power in the "down" motion, you can always assume that is older ITF "tul" stylist.
Kicks: Kukkiwon and modern ITF stylists almost always favor extremely high kicks. As to Kukkiwon, it is written in their textbook that the trend is to favor sparring, and so, this is extended to the forms. As to the ITF stylist, it may conveniently apply to sparring, but the theory seems to be that if you can kick high, you can also kick low. Their reasoning here is a nod toward self-defense rather than sparring - a stark contrast to Kukkiwon/poomsae.
Stance: Kukkiwon, as mentioned, favors sparring, and so speed and dexterity are favored over power and balance. Therefore, their stances are considerably narrow and short. Some schools who hail from Shotokan-influenced instructors (eg: Kukkiwon schools practicing Palgwe forms, Tang Soo Do schools, and some kwan schools identifying little or no affiliation to Kukkiwon) will show very long and wide stances: very powerful, but with a drag on speed and mobility. I can't say for sure, but Karate has a "one strike, one kill" mantra for each of it's techniques, and I surmise the exaggerated stance is a nod toward this mantra.
I think the "tul" crowd is much more moderate, where they do not emphasize the lock to the floor with an extended stance, and yet still retains enough so that mobility and speed aren't sacrificed
Hand Chamber: Kukkiwon/poomsae crowd as well as ITF/sinewave/tul crowd seem universal with regard to hand placement: always on the hip. I don't know the official position on this with regards to Tang Soo Do. The ITF/hyung crowd almost always places the chambered hand at the chest, which is more in line with Shotokan Karate.
Foot chamber: Poomsae crowd tends to de-emphasize the chamber, perhaps as a nod to sparring. While they do chamber - particularly in practice - the forms demonstrated by better performers seem always to short-circuit the chamber. As you might know, a good kicker ought to be able to throw any kick from practically any position, so a chamber is not required, even if desired. This tends to make the form seem less "choppy" and allows it to flow more smoothly.
I have a tendency to see a lot of poomsae performers try to focus on look and feel, and not so much regard to application of movements. With tul performers and many hyung performers, particularly the better students/instructors, you can discern the applications as they do the form. I have a hard time believing most poomsae performers have any inkling what they're really doing in their forms as far as applications are concerned.