1. Short Story: Satire
(Gogol, Twain, etc.)

2. Ridicules/mocks its subject to lower it in reader’s esteem
Satire
Ridicules/mocks its subject to lower it in reader’s esteem
Blends humor, wit, ridicule, spite and irony with a censorious/corrective tone, to inspect human institutions, practices, or foibles and imply improvements/corrections for them
(but does not moralize, as do fable, allegory, etc.)
Sometimes calls for destruction of foolish/inhuman practices, ideas, institutions, etc.
Deals less with “sinners” and criminals than does fools, foolish institutions or practices, frauds, etc.
Not malicious in intent (invective, sarcasm, etc.)

3. FORMAL (direct) satire
Directly attacks a specific person, character, or institution (often by name)
can be
gentle, sympathetic; aims to correct through broad laughter
biting, bitter, and angry; points with contempt to corrupt individuals or organizations/institutions
or mix of both
INDIRECT satire (most frequent kind)
Uses characters (not always representative) who look foolish on their own because of their words/deeds
“pass[es] over a single foe to charge whole armies” (Addison, Spectator #16, March 19, 1711)

4. SATIRE OBEYS ALL OR NONE OF THESE RULES, AT ITS OWN WHIM
Like pornography (for Supreme Court Justice Potter Stewart, at least1), you might not be able to define it or pin it to one definition, but “[you] know it when [you] see it.”
1 Jacobelius Vs. Ohio, 378 U.S. 184 (1964), amendation mine.