As Engels famously noted in Socialism: Utopian and Scientific that there are multiple approaches to what Socialism is. Some socialisms envisage an ethically appropriate ordering of human relations based on collective economic endeavour of some sort, and good associated cultures, and try to implement that plan. Others envisage the maximal development of working class power, economically and in terms of armed struggle, and that future social relations would be determined by the workers themselves (ourselves) based on their power and analysis while taking action.
Communism is normally used to refer to: utopian 19th century religious communities like kibbutz; or, an envisaged future historical process of the working class abolishing property relations; or, to the actual society of the Soviet Union after the 1940s.
In general these words don’t refer so much to specific ideologies, but are used as labels regarding organised political or economic movements in historical societies. They’re terms of social science more than ordered beliefs. And even the participants in these movements view their own ideas as methods of analysis or action rather than beliefs. The “scientific” approach of socialism as class war is more prevalent than the utopian approach of socialism as ideal ethics.
To expand on the specific difference between “socialism” and “communism” compared in the works of Marx and Engels and a number of those subsequently inspired:
For a certain interpretive tendency socialism is an intermediate or early form of workers self-governance and communism is a final or later form of workers self-governance, this time in the full abolition of work and property as social relationships.
What these constitute vary widely, often depending on support or detestation of the existence of wage labour and the state in the Soviet Union.
In contemporary revolutionary politics the call is often put for “FULL COMMUNISM NOW” such as in the 'Callie On The Roof' comic strip, from Pictures For Sad Children webcomic:
Ie: skipping the intermediate relationship of workers being their own bosses. This is from a historical perspective of workers revolutions, hopeful at best.
For this criteria, Socialism would have a direct democratic state of mandated rotating recallable delegate elected workers councils from the factory floor upwards with the sole monopoly on social violence. (Cf: workers councils in Hungary 1956 especially November 4-December 20). These councils would control goods and service distribution on flat wage bases, much like they would control production and exchange democratically with expert advice and very limited production good only markets.
Communism would lack a monopoly on power, wages, classes, and be working on eliminating required labour entirely.
- Engels, F. Socialism: Utopian & Scientific, an extract of Anti-Duhring