There is a classic explanation of the Yiddish terms “schlemiel” and “schlimazel”:
 
“A schlemiel is the guy who spills soup. A schlimazel is the guy he spills it on.”
 
A schlemiel is an inept fool. A schlimazel is a luckless fellow. The soup example has been used since at least 1942.
 
   
A.Word.A.Day with Anu Garg
schlemiel or schlemihl or shlemiel
PRONUNCIATION:
(shluh-MEEL)
MEANING:
noun: An inept, clumsy person: a habitual bungler.
ETYMOLOGY:
From Yiddish shlemil, from Hebrew Shelumiel, a Biblical and Talmudic figure who met an unhappy end, according to the Talmud. Earliest documented use: 1892.
NOTES:
No discussion of schlemiel would be complete without mentioning schlimazel, one prone to having bad luck. In a restaurant, a schlemiel is the waiter who spills soup, and a schlimazel is the diner on whom it lands.
   
A.Word.A.Day with Anu Garg
schlimazel or shlimazel (shli-MAH-zuhl) noun
Someone prone to having extremely bad luck.
[From Yiddish, from shlim (bad, wrong) + mazl (luck). A related term is mazel tov (literally, good luck) used to convey congratulations or best wishes.]
A schlimazel can be concisely described as a born loser. No discussion of schlimazel could be complete without mentioning his counterpart: schlemiel, a habitual bungler. They go together:
A schlemiel is one who always spills his soup, schlimazel is the one on whom it always lands.
         
21 June 1942, Philadelphia (PA) Inquirer, “On Broadway” by Walter Winchell, Amusements sec., pg. 7, col. 2:
The controversy over the word “schlemiel” (Life recently described it as a dope) brought this from word historians: “A schlemiel is not the waiter who spills the soup on the patron, but rather the patron who is unfortunate enough to have the soup spilled on his lap.”
 
28 July 1948, St. Louis (MO) Star-Times, “Jewish Folklore In Both Gay And Sorrowful Vein” by Robert Schulman, pg. 18, col. 8:
(A Treasury of Jewish Folklore by Nathan Ausubel.—ed.)
The “schlimiel” is the awkward, bungling fellow with no skill in coping with a situation. The “schlimazl,” first cousin to the schlimiel, always is plagued by bad luck. Hence, Ausubel quotes an old witticism—“A schlimiel is a man who spills a bowl of hot soup on a schlimazl.”
   
Google Books
Commentary
Volume 10
1950
Pg. 468:
The difference between a shlemiel and a shlimazel is that a shlemiel is the man who spills the hot soup on the shlimazel’s pants.
   
Google Books
The Story of the Jewish Way of Life
By Meyer Levin and Toby K. Kurzband
New York, NY: Behrman House
1959
Pg.. 107:
An old Jewish story explains the difference between these two sad comical characters. “A schlemiel is a fellow who spills a bowl of hot soup on a schlimazel.”
 
26 October 1965, The Globe and Mail (Toronto, ON), “Blastoff To Oblivion” by Dick Beddoes, pg. 34, col. 1:
As an aside, it is pertinent to make a distinction between those splendid words from Jewish humor, schlemiel and schlemozl. A schlemiel is the fellow who invariably spills soup on someone; the schlemozl is the someone on whom soup is spilled.
 
12 October 1970, The Jersey Journal (Jersey City, NJ), “Reds Born Losers In World Series Play” by Jim Murray, pg. 17, col. 1:
CINCINNATI—There is a distinction between the Yiddish words “schlamazel” and “schlemiel.” A friend explained it to me before the game.
 
“A schlamazel,” he said, “is the guy who trips and spills a bucket of soup going upstairs. A schlemiel is the guy he spills it on.”
 
Google Books
Dimboxes, Epopts, and Other Quidams:
Words to Describe Life’s Indescribable People
By David Grambs
New York, NY: Workman Publishing
1986
Pg. 82:
A more Anglo-Saxon word for a fumbler or bumbler is hoddypoll. schlimazl (shli ma’zal) Like the schlemiel, a born loser, but to the nth degree. As the Yiddish saying goes, the schlemiel spills the soup, the schlimazl is the one it gets spilled on.
 
Google Books
Jackie Mason and Raoul Felder’s Survival Guide to New York City
By Jackie Mason and Raoul Lionel Felder
New York, NY: HarperCollins Publishers
1997
Pg. 151:
Schlemiel and Schlimazel (pronounced shleh-MEEL and SHLEH-MAH-zel). These two go hand in hand. There’s a common definition that a schlemiel is someone who spills soup on people, and a schlimazel is someone who gets soup spilled on him.
 
Twitter 
Dave Gray‏
@davegray
The diff between a schlemiel and a schlamazel: The former spills the soup, the latter spills it on himself. 😉 (via @daveixd)
12:16 PM - 21 May 2009
 
YouTube
schlemiel Ron Swanson
Steve
Published on Jun 4, 2012
parks and rec
 
Twitter 
John Corbett‏
@CorComm
The schmuck spills the soup
The schlemiel gets it on him
The nebbish cleans it up
The tummler jokes about it
The mensch pays to dryclean
1:41 AM - 10 Mar 2014
   
Temple Oheb Shalom
What is the Difference between a Schlemiel and a Schlimazal? June 13, 2014
Posted on June 13, 2014
(...)
I will answer with the classic example from Leo Rosten in The Joys of Yiddish. “A schlemiel is one who always spills his soup, a schlimazel is the one on whom it always lands. A schlimazel’s toast always falls butter-side down. A schlemiel always butters his toast on both sides.”
 
A few more examples translated from the Yiddish: If a schlimazal dealt in shrouds, no one would die. If a schlimazal sold umbrellas it would never rain. If a schlimazel dealt in candles, the sun would never go down. A schlimazal falls on his back and breaks his nose. A schlemiel falls over a piece of straw. A schlemiel has a continuing argument with God. A schlemiel cannot even tie a ribbon on a cat’s tail.
 
Twitter
(((Don Amsel)))‏
@DonAmsel
Replying to @MikeStuchbery_
Just FYI -  A schlemiel is the guy who spills soup.  A schlamazel is the guy he spills it on
1:32 PM - 8 Aug 2017
 
NOW (Toronto, ON)
Menashe is a formulaic story with a twist
Minor-key drama was shot clandestinely in Brooklyn’s cloistered Hasidic community
BY NORMAN WILNER AUGUST 9, 2017 5:15 PM
(...)
The old joke is that a schlemiel is the guy who spills the soup, while the schlimazel is the guy who has soup spilled on him.