Political moderate is someone who doesn't align themself with a specific party and judges topics on a case by case basis. That's much more common in real democracies than in the USA's version of democracy, because picking a side becomes a lot more complex when you are dealing with four to six relevant political parties, plus the lack of a binary also means much less push towards a specific side.
I was looking at some survey data yesterday and noticed that the survey listed four optional self-descriptions instead of the usual three: progressive, liberal, moderate, and conservative. I thought it interesting, and appropriate, that 'progressive' and 'liberal' were listed as separate options. I think that's how such queries should be worded because I sense a distinction between the two things. Anyway, the ideological composition of Americans looked like this in the survey:
33% identified as conservatives
31% as moderates
19% as progressives
18% as liberals
Conservative is the most common label Americans identify themselves with, but you'll notice that progressives and liberals combined outnumber them (a combined 37% versus 33%). The party identification part of the same survey also implies that there are more liberals and progressives than there are Democrats and more conservatives than there are Republicans; facts suggesting that not all independents are actually moderates by any stretch of the imagination. That's the point I was getting to with all this, sorry.
Also, I'm actually a card-carrying Democrat myself. It's mostly just my way of being defiant in the face of my state's, and even more especially my particular community's, heavily Republican lean. I have the "TEXAS DEMOCRAT" and "RED STATE DEMOCRAT" bumper stickers on my car to piss people off. I also really liked our last Democratic governor, Ann Richards, for the Robin Hood school funding system she implemented in particular during her one term before being defeated by George W. Bush back in 1994. My school benefited directly from the equitable redistribution of school funds across the state and underwent a very noticeable year-on-year refurbishing and improvement. We haven't had another Democratic governor (or another female governor) since. She was also just a really quirky character of the sort you might suspect I'd like. However, according to this survey's party ID categorizations, I think the most accurate term for me therein would be "weak Democrat", as in am open to voting for Republicans in the future under the right circumstances. (Said circumstances, however, cannot include Donald Trump.) I can think of at least one Republican who has often been named as a prospective candidate for president in 2024 who I might be open to voting for depending on how a hypothetical Joe Biden presidency goes.
But the "judges topics on a case by case basis" part I agree with. That I think is important to qualifying as a moderate and applies to me as well. I just don't think that you have to be independent of political parties per se.