I can think of four things that term might mean; if someone knows of others, I’d like to hear them.
1. A supporter of the Social Democratic Parties, aka the Second International, whence came all of today’s Labor Parties. They were famous for achieving important reforms and sending the workers of “their” country off to slaughter workers from other countries in the name of increased profit for “their” capitalists. Also famous for competing with Stalinism over who has done the most within the workers movement to preserve capitalism. They are rotten through and through. No, I’m not one.
2. Someone who believes the Scandinavian countries are socialist (hint: this requires not living there) and/or believes in a “mixed” economy, which essentially means a kindlier, gentler capitalism. The idea that now, when capitalism is utterly rotten and threatening global catastrophe, and must use every form of depravity and violence to preserve itself, to ask it to be more gentle is, in my opinion, suicidal. As overt white supremacists and fascists revive as defenders of capitalism, this kind of activity strikes me as nothing short of presenting our throats to the wolves.
3. Someone who is in favor of socialism, but either believes, or only supports socialism “insofar as,” it can be achieved electorally. History has taught us a hundred hundred times that ruling classes do not give up their power unless forced to do so, and will destroy democratic forms in a heartbeat if they see that as the only way to preserve their privileges. The state serves the ruling class—that is why it is a ruling class—and a capitalist society means capitalists are the ruling class. They will not go down willingly any more than the slave oligarchy in the US South was willing to. That the economic system they based themselves on was thoroughly rotten and unsustainable only made them more desperate. That’s how it works.
4. Someone who believes, first, that the fight to preserve what democratic rights we still have requires a fight for socialism, second, that socialism is, in fact, democracy consistently applied, and, third, in fighting for a society based on democratic workers control of the state, and of production. By this definition, and only by this definition, could I be called a democratic socialist.