You're not wrong. Where proper socialism seeks to supplant capitalism (and property law) through the power of the state, social democracy instead seeks to exist within the basic capitalistic framework while attempting to curbe its perceived social injustices through state intervention into the market economy and provisioning of social welfare services.

In some respect it's a compromise; mostly in that many of Europe's social democrats emerged from discredited hard core socialist parties. American social democrats, on the other hand, emerged out of a split with liberalism and ironically kept the name.

The distinction is important though. Social democracy in practice translates to simple fiscal policy. Actual socialism would imply a complete overthrow of our judicial and legislative systems.

Whether it is a compromise does not alter the defining characteristics of capitalism and socialism, those being private ownership and communal ownership, respectively, of the means of production and exchange.

These terms are not used as in the vernacular but are precisely defined pieces of economic jargon.