The general problem is that when these ideas and parties first emerged, socialism, communism and even democracy where pretty much utopian ideas without implementations.
Sure Britain technically already had a parliament for some time, but there were still royal prerogatives that were probably more real than they are now, there's literally an upper chamber with the nobility and it took until until 1918/1928 for male/universal suffrage and apparently until 1948 to remove plural voting for property owners and university staff who could vote both in their home constituency and their property/university.
Technically the U.S. had a democratic republic, but then again they also had slavery, racism, the president is a pseudo-king (so electable monarchy without the folklore) and apparently some founding slave owners were so appalled by the idea of democracy that they outright called it "mob rule" and warned that the "tyranny of the majority" could vote to take away their excessive property. While realistically it might have been more aptly described as a tyranny of the wealth white minority:
In the early history of the U.S., most states allowed only white male adult property owners to vote (about 6% of the population). By 1856 property ownership requirements were eliminated in all states, giving suffrage to most white men. However, tax-paying requirements remained in five states until 1860 and in two states until the 20th century (wiki)
Where universal suffrage was achieved or re-achieved as late as 1965.
France was bouncing back and forth between republic and absolutism. Paris had a socialist revolution in 1871 though rather short lived (2 months).
But seriously implementations of the concepts of social contracts, democracies, social welfare systems, republics and so on were scarce and where they existed often left a lot to hope for. Just take a look at when countries achieve universal suffrage. Some male suffrage dates are earlier, but with lots of asterisks such as high age requirements (30+) or property requirements and so on. So most came with the turmoil of the world wars and the following decolonization so early to mid 20th century.
So there was plenty of time and opportunity to build utopian ideas without implementation, to criticize the liberal democracies for failing towards their aspirations or to critique their aspirations for a lack of vision and to argue that if that is what democracy looks like, you'd need a revolution.
And in all of that time you had hundreds of of definitions of socialism, communism or any other sort of workers and welfare movement. Like the first retirement plan was implemented by Bismark in 1881 in combination with a few other social security measures. Largely to take away power from the socialists movements who might have actually had a much more easy time generating a revolutionary sentiment among a population group that worked 10-16 hours a day, 6 days a week (1 day for church), until they couldn't work no more and died of poverty.
So yeah there were hundreds of people and groups in dozens of countries using these terms inflationary and within their local translations, accusing each other of not being revolutionary enough and whatnot. Like apparently for Marx socialism and communism were used interchangeably, also for many socialists it was quite obviously that socialism and democracy are inseparable. They just thought they'd also need to bring the ideal of a republic to the economic sphere, given how apparent it was how lacking democracy can be if it's rigged in favor of the rich.
So before a certain point the usage of "social", "democratic", "socialist", democratic socialist", "social democrat", "communist", "anarchist" was just a matter of preference and priorities. Like for example Marx apparently claimed the term communist and wrote a manifesto for that. Which subsequently lots of people called their strong or weak references to him "Marxism", with Marx himself not always being in favor of "Marxism". His rivalry with the anarchist split the 1st international, though both anarchists and communists might still have called themselves socialists. The internationalism vs nationalism struggle than broke the 2nd international as WWI left them with axis-socialists, allies-socialists and "what the fuck weren't supposed to unite"-socialists. While the reform vs revolution struggle apparently lead to some stressing democracy more while the other still implied that, though where that comes in the name is still a matter of preference.
Also Marx briefly talking about the "dictatorship of the proletariat" which in context just means "government" by the workers rather than the capitalists and an expected period of turmoil after the revolution. While Engels already warned that this approach of a vanguard party and seizing power and implementing shit top down has failed, doesn't work and should be abandoned in favor of a more democratic bottom up approach.
Though apparently Lenin either not having gotten the memo or just not caring about it, does exactly that, vanguard party, coup d'etat and top down implementation. There is the expected turmoil. Many supporting the bolsheviks because hey nows revolution and the czarists suck. Then Lenin's authoritarianism begins to show and that by dictatorship of the proletariat he might actually mean dictatorship (of him). He gets more and more flak from fellow leftists:
https://en.wikipedia.org/wiki/Kronstadt_rebellion
https://en.wikipedia.org/wiki/Left_Socialist-Revolutionaries
After Lenin's death even Trotzky, who was happy gunning down other Leftists in as "counter-revolutionaries", was now on the list of "counter-revolutionaries" ironically for promoting a permanent revolution.
NEP was apparently an attempt to appease the situation after the civil war and to get international grants for Russia's development. The thing is according to Marx the progressions of societies is determined by the material conditions and the mode of production. And so the progression predicted would have been feudalism, liberal revolution towards capitalism, socialist revolution to post-capitalism (aka communism). Though Russia went from feudalism to post-capitalism, at least that was what many thought and so they expected that capitalist interlude and thought Russia wasn't sufficiently developed for communism.
So yeah a mixture of appeasement, experimenting, getting foreign grants and so on. Also Lenin didn't see much of that in the making, he made that plan 1921 in 1922 the civil war ended in in 1923 he had his third stroke and lost the ability to speak and in 1924 he died...
While Stalin mostly coined a lot of the terminology. Calling Lenin's power grap it's own ideology of Marxism-Leninism, the dictatorship of the proletariat "socialism" which would serve as that "turmoil and transition state", with the side effect of justifying him to continue a dictatorship indefinitely. The idea as a whole to restrict that economic system to one country opposed to ... you know "workers of the world unite".
And so the reform vs revolutionary aspect of "social democracy" vs what Stalin now called (real existing) socialism became much more distinct and meaningful.
Though for example the SPD apparently still had claims to nationalize the industry in their party program and it was still common to reference Marx as a social democratic party. So it's not that they were in favor of capitalism, just that they were more willing to do that in the framework of liberal democracy (which had evolved at least something over time). Though there had also already been currents who just wanted better working conditions and a welfare state in whatever system (political or economical), because again times were rough in the late 19th century. So it's more that they evolved apart from each other and that we label them with hindsight knowledge while they at the time might have used many of these terms differently.