Until is the full standard word: The offer runs until Friday. Til is a nonstandard spelling of the casual clipping, which is properly written 'til: Two days 'til the results. They mean exactly the same thing; only the register and the correctness differ.
The core difference
There is no difference in meaning at all. Both point to the moment when a state or action stops: you wait, work, sleep or hold on up to a given time. The difference is entirely one of register and spelling status.
Until is accepted everywhere. Til, with no apostrophe, is not listed as standard and reads as a typo to most editors.
How to use each
- until — anything you would show an employer, a lecturer or a client: Payment is not due until the thirtieth. / She didn't speak until the room was empty.
- 'til — deliberate informality: captions, lyrics, texts, chalkboards. Open 'til late.
- til — best avoided; use one of the two above.
A test for which register you're in
Ask whether the sentence could carry an exclamation mark without embarrassment. Only one sleep 'til Christmas! works. Interest accrues 'til maturity! does not — that sentence wants until.
If you want a form that is short and always safe, use till. It is a standard word with the same meaning, it needs no apostrophe, and it is a letter shorter than until.
Where until earns its extra syllable
Two places genuinely favour the full form. At the start of a sentence, Until reads more cleanly than the alternatives: Until the audit is finished, no invoices go out. And in negative constructions where the timing carries weight, the full word gives the sentence more spine: He did not admit it until confronted.
The common mistake
The real trap is doubling up. Up until is very common in speech and is not wrong, but it is padded — until already contains the sense of "up to". Trim it unless you are drawing a deliberate contrast with what happened afterwards.
The other slip is using until for distance rather than time. English marks distance with up to or as far as: We walked as far as the bridge, not "until the bridge". Time and sequence take until; space usually does not.