This informal argument borrows from formal logic, an enthymeme, the use and abuse of this being also known as the unstated premise, or suppressed premise.
Here, a premise needed to justify the conclusion is absent from the argument's wording. Now, as long as both parties in a discussion assume the same meanings for the terms they use, all is fine.
The problem begins when the two parties do not share the same meanings going into their language, and at least one of them fails to clarify to the other what those assumptions are, whether willfully or not.
It's a good idea to be charitable and not cast aspersions unless willful intellectual dishonesty becomes apparent.
When used to arbitrarily misdefine a word, most often out of ignorance or even some confusion over its accepted meaning, it is known as a Humpty-Dumpty fallacy.
This is often used in conjunction with a multiple untruth, or Gish gallop.
A good example of this are evolution/creationism debates during which the claim is made that:
There are no transitional species between X and Y
Here, the creationist is using a different assumption from his opponent as to what transitional species means, often a sort of half-formed monstrosity 'stuck' between two other species in the fossil record, perhaps the silly 19th century notion of 'one species crossing over into another' fallacy, or the 'dogs giving birth to kittens' nonsense.
Oh, wait, we've discovered those in the fossil record...They're dinosaurs, known as Spinosaurus! Take that, creationists.
The major point here is that the creationist's idea of what a transitional species means, an important bit of information in the argument, has been either overlooked or intentionally concealed from his opponent, the latter being the case with the more rhetorically erudite creationists.
Lest you think I'm only picking on the poor creationists, let's look at a couple of other examples:
Energy can be neither created nor destroyed, so the soul is eternal.
This assumes a vague, undefined notion of 'energy,' completely unlike its use by physicists who invented the term to mean something very specific. Let's not even get into the philosophical and empirical problems with the notion of separable, eternal souls, let alone the further assumption that 'energy' somehow equates to 'soul.'
The existence of antimatter is just a theory.
This hides a premise assuming a non-scientific appropriation of the word 'theory' as something at best like a hypothesis and at worst as a mere hunch arrived at through the use of recreational pharmaceuticals.
Never mind the demostrable fact that the first antiparticle, the positron, was confirmed in a cloud-chamber experiment studying cosmic rays in August of 1932.
It's important to try to find some common ground in any discussion, especially heated ones! When both sides share assumptions going into their language, coming to a resolution to whatever issue started the discussion is much, much easier to achieve.
Be on the lookout, though, for this fallacy when debating ideologues and apologists who though maybe really believing what they say, may not have the full critical skills to reason honestly with themselves or others.
Most people have more concern for feel-good truthiness than with an inconvenient and uncomfortable truth, and it takes concern for truth, courage, and good metacognitive skills to guard against this tendency in oneself.
Tf. Tk. Tts.