It does have a meaning but yeah its kinda missleading, most people just assume is “state doing capitalism” when it just means that the state holds all the political power under a DotP not the capitalist class.

lets take the example of france and china, under the first definition, “state doing capitalism”, both France and China could fall into that category since both have important SOEs and operate under a market economy.

But under the second definition, only China can be categorized as a state capitalist since even though capitalists exist in China, they hold no political power.