Austrian Socialist leader Bruno Pittermann (1905-1983) said in 1961:
 
“The difference between a democracy and a ‘people’s democracy’ is the difference between a jacket and a strait jacket.”
 
A 1970s newspaper columnist reported the line being used in Poland. U.S. President Ronald Reagan said at a Human Rights Day event on December 10, 1986:
 
“The other day, someone told me the difference between a democracy and a people’s democracy. It’s the same difference between a jacket and a straitjacket.”
   
   
Wikipedia: Bruno Pittermann
Dr. Bruno Pittermann (born 3 September 1905 in Vienna; died 19 September 1983 in Vienna) was an Austrian social democrat politician. He served as both the chairman of the Social Democratic Party of Austria from 1957 to 1967, and the Vice Chancellor of Austria from 1957 to 1966. From 1964 to 1976, he was president of the Socialist International.
 
12 October 1961, The Daily Herald (Jasper, MO), “Square Shootin’” by S. E. Stemle, pg. 4, col. 4:
Bruno Pitterman, an Austrian Socialist leader, in characterizing Soviet-bloc countries, said: “The difference between a democracy and a ‘people’s democracy’ is the difference between a jacket and a strait jacket.”
 
21 November 1975, The Daily Gleaner (Kingston, Jamaica), “The Communist,” pg. 30, col. 7:
“I’m sure you haven’t heard the one about the difference between a democracy and a people’s democracy being the same as that betweena jacket and a strait…”
 
Google News Archive
1 January 1977, Sarasota (FL) Herald-Tribune, “Wit Is Index To World Vitality” by John P. Roche, pg. 6-A, col. 4:
The first is a Polish one-liner: “The difference between democracy and people’s democracy is the difference between a jacket and a straitjacket.”
 
11 December 1986, The Times-Picayune (New Orleans, LA), “Reagan raps Soviet repression” (UPI), pg. A-13, cols. 1-4:
In a speech marking Human Rights Day—commemorating the 38th anniversary of the U.N. Universal Declaration of Human Rights and the 195th anniversary of the U.S. Bill of Rights—Reagan touched on oppression around the world.
(...)
The only results of communism, Reagan said, are that “the cupboards are bare and the jails are full.” The difference between a democracy and a “people’s democracy,” he said, is “the same difference between a jacket and a straitjacket.”
   
Google Books
The Dictionary of Conservative Quotations
By Iain Dale
London: Biteback Publishing Ltd.
2013
Pg. ? (Ronald Reagan):
The other day, someone told me the difference between a democracy and a people’s democracy. It’s the same difference between a jacket and a straitjacket.
Remarks at Human Rights Day event, 10 December 1986
 
The Guardian (UK)
Our kind of dictators
Paul Foot
Tuesday 8 June 2004 21.18 EDT
(...)
Reagan specialised in folksy rightwing jokes. He (or his speech writer) once cracked that the difference between democracy and people’s democracy was the difference between a jacket and a straitjacket. He loved democracy, in other words, provided it has nothing to do with people.