Grammar Sam (a.k.a. Sam Beeson) helps tackle when and how to use them, and helps sort out the A.M. P.M. dilemma.
The definition of the two words helps to figure things out to start with.
Acronym: A word formed from the initial letters of words in a set phrase. (ASAP, RSVP)
Abbreviation: A shortened form of a word or phrase. (Dr. Mrs. Prof.)
One abbreviation which most get wrong is TV; it doesn’t take periods. For a list, consult a dictionary or reference volume such as The Oxford Dictionary of Abbreviations.
For a world of wacky “truth” about these and other rules, see Dave Barry’s column: