What do socialism and capitalism mean to you and has your understanding of these words changed since you first encountered them?
I'll answer the latter question first: Yes, my understanding has changed.
My earliest exposure was based on Germany and the Soviet Union both incorporating "socialist" into their parties, in ways that seemed pretty anti-social to me. Also, totally wrong, of course. Then for a long time I thought of it as "communism light" based on the technical definition of socialism as being social control of the means of production - which I did (and still do) think is an abysmal idea.
As I've gotten older, I've kind of scrapped all the academic jargon and the politically charged views. Both are ways of organizing an economy. Capitalism refers to a system where the consumer drives the bus - whatever sells is what gets made, whatever sells better gets made more. Socialism refers to a system where the government drives the bus - whatever is needed gets made, and whatever is needed more gets made more. Neither is a perfect view, but in practice that seems to be the core of it.
In terms of reality... neither is perfect, and they both have their role. I tend to favor a largely capitalist structure for most trade. I think that the concepts behind it are best suited to human nature, and they provide a reasonable means to provide options and choice to the greatest number of people. But left completely unfettered, there's opportunity for exploitation in all sorts of ways. There are a lot of potential pitfalls, but to me the largest fall into a few categories.
There's the risk of very large companies taking a monopoly role in the market, which then gobbles up all the surplus value that makes the whole thing work. This is particularly problematic when those monopolies are associated with services that most people would consider necessary - water, power, sanitation, etc.
Then there's the risk of what I'll call "silent collusion" between large players within a particular industry, where the companies involved all realize that they can collectively push the price of something up and they all win as long as nobody rocks the boat. It's not direct collusion, there's no meetings about it. It's just sort of something that happens. This happens a lot when there's a bit of a middle man involved, and it tends to more often be the primary suppliers upping the costs to the middle men, who then pass it on to the end customer. I see this a lot in the health care industry, with pharmaceuticals and medical devices. The primary manufacturers know that there's a middle-man who spreads the cost risk, and they take full advantage of it. Customer end up angry at the insurers for the high price of health care, even though it is being driven by the profit margins at the provider end of the deal.
There are others, but I think this captures the problem - there's a risk of bad actors exploiting loopholes and basically profiteering.
When it comes to socialism, it has the opposite problem - lack of choice. This can lead to quality-related pitfalls, as well as sometimes the government thinking it knows what is important to people and being wrong about it. In many parts of the US, water and power are effectively socialized industries. We usually only have one choice for those services... and if they suck then you're just screwed.
Socialism can also lead to resource constraints that aren't always necessary. I end up going back to my area of expertise, because it's where I have the most concrete knowledge... so health care again. One common refrain we hear from UK and Canada is excessively long wait times, sometimes not being able to get access to a doctor, sometimes being denied care that is quality of life but not directly life saving (like knee surgeries and similar things that reduce pain and increase mobility, but they don't actually make you dead if they're not fixed).
By themselves, both of those can lead to problems. So over the years, I've ended up favoring a hybrid. I tend to want essential services to be socialized, but with civilian oversight committees with term limits so you don't end up with entrenched interests playing games. I think the oversight is necessary so that quality and resources can be addressed by representatives of the people actually using those services. I think it would also be a good idea to have multiple committees that vary by geography - not all parts of the country are going to have the same needs at the same times.
On the other hand, I'd like to see most non-essential businesses continue to be privately owned (also employee owned if a company wants to be). It increases competition and innovation. I also think that the "capital" element of capitalism - the investment in new ideas and in young companies - is something that is unlikely to come from a highly socialized system. You've got to have at least some people with enough extra cash that they're willing to take bets on something that might not work out - and that's something that the government shouldn't do with taxpayer money in my opinion.
So circling back to my sphere of knowledge, I'd love to see providers of health care socialized. I'd like to see the doctors, nurses, and other professional practitioners be government employees, paid a salary. Same with facilities - hospitals, urgent care centers, imaging centers, etc. would be government owned and government run. Medical supplies and pharmaceuticals should be negotiated at the federal level. This would help control primary costs. I think there's still a need for consumer oversight to make sure that government wages and payment levels aren't making it impossible to stay in business.
I would pair this with a subsidized health insurance system - something more akin to Medicare than current ACA is. A core set of reasonable benefits, with reasonable cost sharing for customers (helps to manage over utilization). But also allow private insurance to wrap around or to replace it, same as we do with Medicare Supplement and Medicare Advantage today. There would still be a lot of available choice, so that those who need more care can manage their financial investment in it, and those who don't use care aren't being charged so much that it risks bankruptcy. This would then also have government oversight - to make sure that insurance companies aren't exploiting customers or lining their pockets in an abusive way.
So yeah, really long answer. That's essentially how I perceive socialism and capitalism to be in the real world, outside of academic notions.