I have noticed a separate disagreement about what capitalism means, between me and a family member.

I used to think of it as how you handle your private economy. If you are a capitalist, it means that when you have surplus, you save it up and use it (as capital) to improve your future, i.e. you invest it. The main alternative is to be a consumer, who simply spend it all.

My family member sees capitalism as something like big corporations that advertise and make you spend money on things you don’t need. She sees consumerism and capitalism as basically the same thing, while I see them as complete opposites.

"Capitalism" or even "late-stage capitalism" is currently a pure negative connotation terms among the progressives in the West, with no denotation left. Your definition is also non-central, compared to the original and more standard "Capitalism is an economic system based on the private ownership of the means of production and their operation for profit." This, incidentally, includes social democracy.