Not sure how you are defining them, but they are, and aren't, the same. Socialism is a transitionary government to communism. It isnt the 'exact' same thing, but when a communist party is in charge, they create socialism, with goals to move towards communism.

Socialism is also a lot of things, but all those things are considered communist.

Democratic socialism is what Cuba has for example. Socialism run by a democracy.

Socialist democracy is what Sweden has, currently. It's still capitalist, so is not communist at all, but regulates capitalism better than America and most of Europe does. They are slowly loosing the fight to Nazis though. Like literal Nazis, they call themselves nazis, That's not a joke.