I have not heard of equivalence between „Soviet“ and „People’s democracy“ before. In fact those terms are mutually exclusive. Either your country has multi-party system, at least formally, or it is a Soviet republic.
"People's democracy" is actually the regime when there's a single ruling party system but it calls itself democratic because it is comprised of, you know, the people.
It is literally in the first paragraph of the Wikipedia article:
People's democracy is a theoretical concept within Marxism–Leninism and a form of government which developed after World War II and allows in theory for a multi-class and multi-party democracy on the pathway to socialism.
The German Democratic Republic had a plural multi-party system. The largest by members and parliament seats were the Socialist Unity Party of Germany (SED), followed by Christian Democratic Union of Germany (CDU) and the Liberal Democratic Party of Germany (LDPD).