Like with all things, it’s a matter of degree. Democracy and socialism are not inherently incompatible, but can be mixed together at different ratios. For example, a democratic socialist society could follow in the Swiss model of direct democracy, meaning everyone has a say in the policy decisions. Such policy decisions include the law but also how to utilize the means of production, which the state owns entirely.

Whereas another democratic socialist society could realize their democracy through a representative model, where citizens elect a local representative that goes to the capital and votes in a state committee on how to amend the law or utilize the means of production, which the state owns entirely. Here, political power is wielded by a committee but the complete socialist ownership is intact.

Yet another democratic socialist society could be much softer on the state ownership of all the means of production. The state might own the utilities, roads, schools, and all land, but may permit certain collectives to privately own businesses that generate value and to distribute those earnings equally amongst themselves. This could be considered a transitional step, since it allows for a controlled amount of capitalist-style development to occur, while avoiding huge concentrations of private capital. But it could also be a step backwards if the state already fully-owned the means of production but then voted to release some of it to small co-ops.

While words have to mean something to be useful at all, I wouldn’t spend too much time trying to fit all possibilities into neat categories. Ultimately, socioeconomics are fluid.