A Few Practical Chess Insights For Intermediate Players

At the lower level the main issue is to get rid of blunders, usuallty caused by playing too fast.
At the next level the main issue is tactics 1 move deep, 2 moves deep, 3 moves deep.
The next level is endgames: learning how to win with an extra pawn, how to draw when a pawn behind, how to play against a wekness, how to defend a weakness.

"I'm mainly interested in understanding insights into how an intermediate player can improve."

When you're looking for quick results, you should study your own games, look for your mistakes and make sure you don't repead them.
-you get mated after just a few moves->study openings
-you get a bad but playable position after the opening, an ok-middlegame, win the queen with brilliant tactics but then you stalemate your opponent->learn basic endings.
-you know how to mate with bishop and knight, but you never get an ending, because you're always getting mated in the middlegame->learn tactics/middlegame plans

Also your attitude has influence: You improve faster if you really want to improve. There are lots of players who play just for fun, not for improvement, and they improve very slowly. I once decided to either win a game or to learn (or both).

@jonesmh
I "condemn basic tactics"?? What reading comprehension problem led you to that delusion?
I OBSERVED that masters often hang pieces, which seems contrary to beginner advice, because they get an overwhelming advantage (such as checkmate! As Ben Finegold says, "mate with advantage") if you try to take the piece. Those are themselves tactics. Incidentally, my first aggressive move there, after ...Bd6 Ng5, I first learnt from a Finegold lecture on openings, and confirmed with my old coach stockfish. I used to play defensively against black's alignment of B and Q. Which reminds me of another insight: STRONG PLAYERS ALWAYS LOOK FOR OFFENSIVE MOVES TO COUNTER OFFENSIVE MOVES. In other words, they live by the motto, the best defense is offense.

@Der-Wir-Ing

I meant I'm interested in particular chess insights such as those I mentioned in my OP or above, not general motivational advice about wanting to improve and correcting one's mistakes.

@tpr That's true. I'm finding against higher rated players I often lose the end game, or let them draw when I should have won, or fail to force a draw myself. I've noticed Stockfish has an impressive array of tactics for forcing a draw when down material; I should find a way to study those somewhere systematically. Maybe engame books....

" STRONG PLAYERS ALWAYS LOOK FOR OFFENSIVE MOVES TO COUNTER OFFENSIVE MOVES"

A Beginner just reacts to his opponents moves. Only later you're able to create your own (counter-)threads. Stronger players know when a possible counter-attack is stronger than the opponent's and when not. Stronger players know that in general aktive play (attack) is best, but the really strong player knows when to defend passively is best. They might "always look" for offensive moves, but they don't always play them. For example after 1. e4 e5 2. Nf3 the petroff defense 2. ... Nf6 is an agressive counter-attack. But the masters prefer more passive defenses with 2. ... Nc6 wich offers a better defense and also good chances for a later attack.

Be carefull with words like "always" or "never", especially in capital letters.

When you have positions with opposite side castling, in general your best plan is to agressively attack your opponents king by advancing pawns even when you have to sacrifice pawns or pieces. In positions with same side castling and closed center in gerneral you should do the opposite: Slowly manouver your pieces to better squares. The true master knows when to make a "slow" move during an attack and when to sacrifice in a positional game. Strong players know wich plans are best in a positon.

A strong player reacts to his opponent's plans before the opponent plays them

@Der-Wir-Ing

"Be carefull with words like "always" or "never", especially in capital letters."

Did I not? You agree with what I said: a strong player always looks for offensive moves to counter offensive moves. As you observed, they will not always play them; I was well aware of that when I chose my words. Obviously a GM will make a defensive move when called for.

@blindlyzerking Yes. They are always considering what the opponent might do, both immediately and in terms of plans.

@nayf yes, a strong player won't necessarily defend with an "attack", however active defense is often employed, as passive defense can often lead to disadvantage

@blindlyzerking The more general principle is that taking the initiative is generally better than playing defensively against an opponent's initiative. I think that is because taking initiative typically means creating threats, and creating threats increases the probability of finding winning tactics. So if one can reply to threats by creating threats of one's own, that is typically preferable. But of course it is not always the optimal strategy.

Intermediate players do not understand the vital importance of having a plan... pre-game plan, opening-phase plan, middlegame plan, and endgame plan. The Master's understand that the mind needs a plan to operate at maximum potential... the mind needs a plan to activate visualization processes...and this leads to seeing the whole board... and finding the best move. Beginners just shoot from the hip... they close their eyes and throw a punch... they are mindless woodpushers without a plan. Intermediate players have some level of knowledge, experience, and rudimentary concepts that serve as ad hoc plans, but they also they have all kinds of bad habits that need to be purged.

Be patient.