what's the main difference between a 1300 and a 1800 player?

The main difference is that the 1800 is a patzer who thinks he or she is skilled, while the 1300 is only a beginner.

I went to 1901 in less than two years, and I still am underrated, providing I perform against masters like I have so far.

Why was this thread revived again? 

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Oooooh, now you are talking EXPENSIVE...

This thread was dead and buried. Why dig up the coffin?

My opinion, is that 1800 is not that much better than 1300 (if he were years that rating), specially not in every aspect of the game. For instance when i was 1300 i did not know where my pieces belong - N on d2 or c3  Now i know if there are pawns on c6 and d5 n on c3 is bad, but still make plenty of positional errors. I did not know openings back then , and i can say i do not know them well yet. If i am d4 player and i play 1.e4 e5 2. f4 exf4 i could be crush by lower rated 12y old little girl in less than 15 moves. For endgames -  I just recently learned king and pawn endgame vs king. And here are many 1400-1800 blitz and rapid players who dont know it. Most of the games were basically over before reaching such theoretic endgames. When you go up at rating ladder you start notice not how much you know, but how much you dont know.

But for sure i can tell i am a lot better at tactics and patterns and overall awereness of what is going on and evalation of position and though process (except openings). Back 2-3 years ago i would hang a queen and a rook at same game. i had to slap myself or put water on my face, becouse i would lose track in messy positions (knighs forks so hard to spot), even if i had plenty of time to think i would still blunder like crazy. That's why for beginners i recomment more blitz games and tactics - thats what really matters at that level, but first watch how to play correctly blitz by masters with comentary from youtube. Thats how i improved. I abandoned slow time controls but now i am quiting bullet and blitz.

A 1800 player has 14 lower Average Centipawn Loss wich is not a huge difference.But ACL doesnt care about openings so i would say better understanding of opening and endgames also slightly better overal play.

The 1800 player will not miss a simple tactic as easily as a 1300 and understands better strategy and endgames. This article written by a 2000+ player explains everything according to the level.

That article puts too much emphasis on openings, fails to recommend tactics training until a player is over 1400, and generally lacks descriptions of the characteristic weaknesses of each level. Aside from those flaws, it is not too bad.

less tactical mistakes and a better positinal point of view I guess

In my opinion the 1300 player tends to get lost in the middle game especially when the position goes off book, thats what happens to me

You didn't notice what it says.

1200-1399: Study more openings, but do not stick with “rarely played variations”. It is a huge mistake that a LOT of chess player make while studying openings, to study rarely played/unusual lines which most likely would never come up in real life tournaments.  Studying standard opening lines would yield a lot more results!
Spend maximum of 20% of your study time to study openings. Until 1800 level openings aren’t very important. Concentrate more on middle game and tactics.

Where does this come from? Is there any public studies about ACL <-> rating correlations (for lower rated player).

realistically, it's a little bit of everything. there's no magic to get you to 1800, or any other rating.

Indeed. I think ratings are relative. I don't play chess competitively anymore nor study. It's just a hobby. My rating is just an indicator on this site how experienced I am. 30+ yrs. I imagine anyone who is rated 1300 on this site wanting to improve to say, 1800 (or beyond) and is relatively new to chess overall, is going to go through some growing pains. Back in my day, I never had as many resources as we do now, if one was interested in improving you had to go get it. Books, tourneys, a love for the game and an often on again & off again commitment.

In hindsight, I can honestly say I studied more than I improved. Pattern recognition is to me, stifling.

Studying a fair amount of tactics, combos, which is to say not make it a priority, is all you need. Essential endgame principles, positions is key. Mainline of openings is sufficient. In competition, of course keeping up with current trends is a no brainer. But for self improvement, I absolutely believe less is more.

The 1300 is a couple of years (maybe more) younger than the 1800.

I have a 1362 fiderated 56  year old friend , and it looks like he reaches 1800 when he gets 58, after five years of competing otb.

fewer mistakes and consideration of more number of moves