So how does Socialism, Marxism and Communism differ?
I was told Leninism and Maoism are the same, and Bolshievism and Stalinism are the same.
For anyone who is interested, here is my take.
Socialism is a term for a very broad set of political ideas, principles and beliefs. It's use is so varied and vague that it means different things to different speakers and can amount to just about anything.
For the most part a modern socialist political party or movement stands on a platform of redistribution (generally by taxation and selective nationalisation), workers rights (via unionisation though having workers representation on boards and worker equity share are becoming popular), and reliable access to health care, housing, welfare, and work. Internationalism, opposition to imperialism and war, and a recognition of the class struggle going on in every society are common.
I'm a socialist because I support the right of workers and working class a whole to organise and negotiate collectively. I really want a market economy with a higher proportion of cooperatives and worker owned companies - supported by legislation and tax policy that prefers local, worker owned enterprise. Also the public ownership of public goods (including land, energy, transport etc) and a redistributionist economic policy and a guarantee to every member of society of decent housing, health care and education.
In a more narrow sense socialism can also refer specifically to the ownership and control of the means of production by the workers. This is where Marxism become relevant. Marxism is the political theory that history of society is really just the history of class struggle and that each advancement of society (revolution etc) has come about through the victory of one class over another i.e. the capitalist mode of society came about through the victory of the bourgeoisie over feudalism and the land-owning aristocracy. The Marxist analysis concludes that the capitalist class will create a new class that will in turn overthrow the capitalists, seize the means of production and end the class war for good. That class is the proletariat or the workers. The person who subscribes to this idea is a Marxist.
The history of the adoption and "implementation" of Marxism is another messy story but if I had to shorten it I'd say this, Marxism is like a prophetic fairytale and trying to implement it as policy is bound to be a complete disaster.