What a neatly succinct way to put your understanding, well phrased.

It's unfortunately conflating economic policy with social policy, and is quite divorced from anything happening since 1917. Most of Europe lives in democratic socialism, which combines none of A), with none of B).

From the power perspective you're mostly right though, in socialism it's the citizen that has rights, in capitalism it's capital. Meaning that voting and influence stems from different fundamental perspectives, sometimes different enough that they aren't opposed (like in most western DemSoc).

Economic socialism typically means that the purpose of the economy is to raise the standard of living for the citizens, this typically means providing healthcare, infrastructure like roads, housing and clean water, and affordable goods. And usually leads to equalising tax structures, with progressive taxation of the affluent, and higher tax burden in the things that exploit/hinder the societal good, like companies, damaging luxuries (like alcohol, sugar) and pollution.

Ideologically it typically means that every citizen has the right to a comfortable and fulfilling life, where emphasis and understanding differs across the world. And it typically translates to citizens having equal, unalienable rights, with support structures in place for the more vulnerable. That could be that official documents are made available in multiple languages, more flexible voting arrangements, advocacy and support for infirm, elderly and marginalised groups. I'd simplify it as: every citizen is entitled to a comfortable and fulfilling life, and all the support they need to live it.

Politically the focus is on common good, with as little individual impingement as possible. Universal healthcare and education are great investments in the national economy, so is child and elder care, which frees up the workforce from other chores. Support for the arts, hobbies, and recreational spaces is common, as is public beautification, public forums, parks/nature preserves.

But none of this is in necessary opposition to capitalism, which isn't a political system of governance more than economic anarchy. Capitalism doesn't by itself have any aims, ideology, or principles about voting rights, it simply wants capital to produce more capital, and would in the extreme not have any voting rights beyond what you can create with your capital.

In the US it translates through liberalism to policy, where small governance leaves more room for individually powerful citizens, of which capital is increasingly the dominant party.