Am I on the right track there or not so much?
It does. It is social ownership of the means of production. As a democratic socialist AOC believes in worker ownership and democratically controlled market entities. Accordingly, she is very pro-union and pro government jobs programs. The GND has many aspects of a socialist jobs program. Free trade and higher education is a socialist position as well as a welfare position. Medicare for all is socialized insurance. 70% marginal tax rate is a way to limit the concentration of individual wealth and market/political control and while it is not inherently socialist it is extremely consistent with socialist values.
The UK has nationalized healthcare- doctors are literally employees of the government. It doesn't really get more socialist than that, but it's still just a single program. The government as a whole, and the country as a whole, leans significantly more towards liberal capitalism.
Very few terms that refer to current (as opposed to purely historical) movements or identity groups have single, universally accepted, strict definitions. That's true or “socialism”, it's true of “capitalism”, it's true of “Christianity”.
> AOC for example claims the label socialist, but as far as I can tell she’s not actually taken any socialist policy positions.
AOC is a member of the Democratic Socialists of America, which recently left the Socialist International because it viewed the latter as having slipped too far to the right and abandoned socialism by endorsing what the DSA saw as neoliberal economic policies. So, the DSA is to the left, ideologically, of the main global organization of socialist parties and groups.
Now, the DSA is also very much an incrementalist organization that sees socialism as a long-range goal, favoring what could easily be seen as evolutionary socialism. And AOC is one of I think three socialists between both houses of Congress, so it's not like even if she was an “as fast as possible” socialist ideologically she’d achieve much by, say, tabling a resolution to amend the Constitution to abolish private property in the means of production.