horizon effect i suppose
Stockfish marking its own moves as imperfect.

I find it dumb that stockfish can rate it’s own moves as an inaccuracy, just adding more against the crappy game review

You see the effect of different content of the transposition table (hash table). During analysis the engine in effect plays both colors, so it visits and stores in the hash table significantly more nodes.
You would have to use a chess GUI that allows the single copy of the engine to play both sides, not the engine plays itself by running two copies, one for each color.
The alternative is to issue "setoption name Clear Hash" to have the engine forget previously visited nodes before making or analyzing each move.

Huh, it analyzes differently depending on which color it is? Also, which is more accurate; the game playing stockfish or the analyzing stockfish?

This can happen due to 2 (3) reasons.
1. The report engine doesn't see the same as the playing engine. Maybe the report engine, even at the highest depth 30 (making a comparison between the lower depth engines and the playing engine is useless) it can evaluate some lines (slightly). This can make it think one line is better or worse, when in reality it isn't. For 99.999% of all games reviewed, this depth difference doesn't matter anything, stockfish changes from 3540 rated to ~3200 rated. And if you're strong enough to see stockfish misevaluate a move, strong enough to know to analyse with a higher depth.
2. You're evaluating past games. Since last versions, stockfish has gotten immensely stronger over the past years. It'll detect errors in its games, simply because it's stronger now.
(3.) The playing engine was actually incorrect. This rarely/never happens. For one reason, stockfish is currently the absolute best engine out there, and with a level playing field, it comes far out on top.

Huh, it analyzes differently depending on which color it is? Also, which is more accurate; the game playing stockfish or the analyzing stockfish?
No. it doesn't analyze differently depending on which color.
Normally, when you play engine against some opponent the playing engine always gets surprised with the opponent move because it doesn't think of anything when it is the opponent turn. (Some GUIs have option to allow the engine to think on the opponent's time).
When you are analyzing the engine in effect puts the same amount of thought/search into both sides of the game, so it is never surprised by the opponent's move.
So, you can think of analyzing engine as more accurate.
You can further increase the accuracy of analysis by doing self-analysis backwards from the last move to the first move. This in effect makes the analysis engine prescient because it always correctly knows the opponent's move.
Title, I’m curious why. When stockfish goes up against another engine, it makes moves. Then, when I analyze those games after, even with stockfish running at full depth, I’ve seem stockfish mark its own moves with “great”, “good”, and even “inaccuracy”. (I have never seen it mark a move as a mistake.) Why is this? If the engine playing and the engine analyzing are both at the same depth, it doesn’t make sense to me.