Learn English – How to choose an abbreviation for a given word

The simple answer is, you can't. If you are having a conversation with someone who uses an acronym, the only way you'd know is if they spelled out the letters. Otherwise, you'd simply have to ask. And obviously used in written form such as an e-mail, you'd never know if it were an acronym outside of context. Though a good list can be found here.

A good rule of thumb is that acronyms that might look difficult to sound out are likely spelled instead (FBI, FDA, IBM to name a few).

In materiel management these distinct concepts of "unit" are called the "Unit of Measure" (U/M or UOM) and "Unit of Issue" (U/I or UOI), but these terms may be unfamiliar to some.

ORIGINAL ANSWER assumed a medical context, kept here for posterity:

In a medical context, I'd be careful not to use any abbreviations that could be ambiguous. In particular, there is another meaning of the word "units" in pharmacy:

Unit 1 - a category of measurements, like kilograms, and miles.

Unit 2 - piece, item

Unit 3 - abbreviated U, or often International Unit (IU), an "unit of measurement for the amount of a substance, based on biological activity or effect." Different drugs have different-sized U's.

If you were to use the abbreviation U you might run into confusion with the last definition.