The Dilemma: You just stubbed your toe or opened your 401(k) statement and you want to let loose with some language that would make a sailor blush. Which category do those colorful words fall under?
People You Can Impress: Sailors, legal scholars, linguists.
The Quick Trick: Who's mad at you for saying what you said? Obscenity gets you in trouble with the law. Profanity gets you in trouble with religious folks and The Powers That Be. Vulgarity just gets you in trouble with your mother.
The Explanation: Obscenity (from the Latin obscenus, meaning "foul, repulsive, detestable") generally covers sexual or scatological references to the body or bodily functions (i.e. F*&k and s#$t). The term is also used in a legal context to describe expressions (whether words, images or actions) that offend the sexual morality of a given time and place and are not protected by the First Amendment.
In this legal context, though, we're still grappling with what counts as obscene and what does not.
Former Supreme Court Justice Potter Stewart once famously said that he couldn't define what kind of material was obscene, but he knew it when he saw it. We've came little further with the Miller Test, which comes from the 1973 ruling of the Supreme Court case of Miller v. California. If an expression meets these three criteria, then it's obscene:
1. The average person, applying contemporary community standards, would find that the work, taken as a whole, appeals to the prurient interest.
2. The work depicts/describes, in a patently offensive way, sexual conduct or excretory functions specifically defined by applicable state law.
3. The work, taken as a whole, lacks serious literary, artistic, political or scientific value.
If the expression fails to meet any one of those criteria, then you're off the hook. "Average person," "community standards," "patently offensive" and "serious value" are all fairly subjective terms, though. Even with the Miller Test, there's no national standard for what classifies as obscene, and distinctions between protected expression and unprotected obscene expression vary among federal court districts.
If you're being profane, you don't need to worry about the Supreme Court (it has no legal definition), but if you believe in an immortal soul, you might be in trouble. Profane (from the Latin profanes, meaning "outside the temple") originally referred to things not belonging to the church. Later it meant blasphemy, sacrilege or taking the Lord's name in vain (we just call that blasphemy now).
Today, profanity is an expression that is specifically offensive to members of a religious group. The definition also extends to expressions that are scatological, derogatory, racist, sexist, or sexual. What is and isn't profane largely depends on the context and the company you keep.
Finally, vulgarity (from the Latin vulgis, meaning "the common people,"), which used to refer to text written in a vernacular instead of Latin, has two definitions today, depending on who you ask. For some, vulgarity is generally coarse or crude language. For others, it is more specifically the act of substituting a coarse word in a context where a more refined expression would be expected.