Hmmm...... Now, this is not the textbook definition by any means, but how about we just use socialist to mean two things, since no one can seem to agree on what it means in the first place:
Socialist:
1. A person who particularly believes in or pushes government regulation and control, of the economy specifically
AND/OR
2. A person who particularly promotes social programs (i.e. welfare state sort of stuff)
Sure, no textbook definition, but it definitely covers basically everything which people often call socialist. Most communists governments had similar policies at least in theory, the Nazis have a twisted-screwed-up version of this ideology (Their name is the "National Socialist Worker's Party", after all), the welfare states of Scandinavia, and the Democrats (especially Bernie Sanders). Not saying they are all the same, just have a somewhat similar feature of their beliefs. Socialism is often less a state or idea of government by itself and more a feature of larger ideologies.
Also, welfare state here is not the derogatory Republican term it might be, but the idea that the state should do everything it can to guarantee the well-being of it's people.