Both are federations, in that direct members of each are autonomous organizations. But there isn't just WTF and ITF, because there are at least 3 ITF organizations:
one hq'ed in South Korea which is not a federation;
one hq'ed in Benidorm, Spain (www.tkd-itf.org) which is a federation (its members are themselves federations: North America & Carribean, Asia, Europe, Africa, Oceana, and Central & South America);
and another in Vienna, Austria (www.itftkd.org) and which is also a federation (its direct members are themselves federations: Asia, Oceana, Europe, Pan-America, and Africa).
Similarly, WTF is also comprised of federated direct members, making the hierarchy similar. Note, then, the only ITF organization that is NOT a federation is South Korea.
From a student member point of view, there is little difference between them. Their dan issuance comes from the HQ of the federation in which their school is affiliated.
You should also know that WTF isn't a style. That is because dan and instructor certification are governed by a different authority, which is Kukkiwon, based in Seoul, S Korea. That means technically, the style is called "Kukkiwon", not "WTF". However, WTF is a valid organization - and federation - and so, it's not appropriate to distinguish between technical differences.
The reason? ITF members are welcome to join WTF. WTF is charted solely for the purpose of competition, which includes the Olympics. With a bit of paperwork, one who is a registered dan-certificate holder of any of the ITF organizations may apply for dan certification at Kukkiwon (a necessary element to compete in WTF competitions).
As to the rules? That depends entirely on the tourny. Some ITF competitions allow punches to the face and back of the head, others dont. Some require chest gear, others make them optional. Each has point and warning differences. Between all of the federations, the rules are similar - but not identical. Size of mats, qualification for coaches, age categories, weight classes, skill classes, round timing... they differ. They get more consistent when the competition gets more formal, particularly with regards to Olympics.
From a style perspective, though, there are guidelines, because it's not common to see ITF members join WTF.
ITF students almost universally practice the Chang Hon set of forms (sometimes called the "Chon Ji" set, named after the first form learned). Whether the student applies the sine wave (and calls the set of forms "tul") or not (and calls the set of forms "hyung") is a guideline set by the school, although formally, all ITF federations adopt the sinewave methods.
WTF doesn't have forms. Only sparring.
But if you considered Kukkiwon, then the set of forms learned is "Taeguek", a set of underbelt forms which replaced an older set of underbelt forms, called "Palgwe". Some schools practice both sets of forms. In either case, the schools almost always practice the black belt forms beginning with "Koryo".
Another difference between them is that WTF is by far the more commonly seen taught in the US. Where this may be different elsewhere, I don't know, although because of the Olympics, my bet is that WTF is the more common around the world.
Because WTF is not technically a style, and because they concern themselves only with sparring (not forms), they technically don't have a self-defense program, either. Self-defense and sport have overlapping concepts, but strategically, they're very different. ITF does have self-defense, if you carefully study their forms and have a good instructor. WTF schools might incorporate self-defense, but, that teaching does not come from WTF, it comes from the instructor's knowledge from elsewhere - perhaps from Kukkiwon's forms.
So recently, the US Olympics for Taekwondo (Team USA) - that is, the US branch of the WTF - has now opened membership to Taekwondo competition to any ITF and ATA ranked individual.
USA Taekwondo Announces New National Dan Program
The way it works is this: to compete, you need to be a certified black belt. Traditionally, your rank came from Kukkiwon. Now, a new program, called the US National Dan program, allows its members to get an equivalent dan certification that can be used for WTF competition. At this time, only ITF and ATA certified rank holders are eligible, and the criteria for other organizations is spelled out in the by-laws.
This might cloud the difference between ITF and WTF, but the difference is still that WTF is not a style, it's a federation whose purpose is the conduit for international and Olympics Taekwondo competition. ITF member students are now allowed to compete in the Olympics, per the by-laws spelled out in the link.
Basically, as far as Olympic competition is concerned, ITF, ATA, and Kukkiwon are all on the same playing field as far as opportunity to compete in the Olympics. Prior to this announcement, any ITF or ATA (or Karate, etc) student who wanted to compete in the Olympics had to join a bona-fide WTF school. Now, you just need to have a ITF- or ATA-certified dan rank to compete.