Pressing is a complex topic, a mix of science and art. There are many choices that produce different desired outcomes.
Get a glass of wine (maybe 2) before continuing -- this is a long post!
When to press? The longer the fermenting wine has contact with the pomace, the more constituents it extracts from the pomace. To produce a heavier, fuller bodied, and more tannic wine -- press after fermentation ends. I've heard of folks leaving the pomace in the wine for weeks after fermentation to get the most body.
I prefer to press when the SG is 1.000 or below, but fermentation not complete. The cap is still solid so I can rack a lot of the free run wine from beneath the cap. This means I put less "stuff" in the press, e.g., less labor.
People press at higher SG as the heaviest wine is NOT necessarily the goal. Also, free time matters e.g., it's Sunday, the SG is 1.010 and I will be working 12 hour days until Friday. So I'm pressing today.
Free run wine has less harshness than pressed wine and can have a "cleaner" aroma and flavor. It also has less aroma, flavor, and body. Hard pressed wine has more of everything, including a harshness, so it's a trade-off. Some folks age the free run and pressed wine separately, and blend in some of the pressed wine into the free run to increase body without increasing harshness too much.
For 2020, I have one barrel that is 2/3 Merlot, 1/3 Vinifera Blend (Cab Sauv, Cab Franc, Malbec, Petit Verdot), all free run. The second barrel is 40% Merlot, 40% Zinfandel, 20% Vinifera Blend, all medium press. Beyond the difference the Zin makes, the wines are clearly different. [I like experiments and can seriously complicate my wine making life by getting deeply into things.] I'm pleased with both so far, as they give me an interesting variety in the cellar.
NOT pressing throws away a lot of wine. I produce a 2nd run from the pomace, adding water, sugar, tannin, and acid to produce about 50% more wine -- wine that is lighter in color, aroma, body, and taste -- and ages quicker. "2nd run is what ya drink while the 1st is aging"
Last October I added 15 gallons of water + sugar/tannin/acid to the pomace from 16 lugs of grapes. When I pressed it, I got ~20 gallons of wine, meaning that the "medium" press I did for the 1st run left 5 gallons of wine in the pomace.
In 2019 I divided the press for the 2nd run into 2 parts -- 15 gallons of "medium" press and 7 gallons of "hard" press, where we cranked the press hard to get what we could from it. The 2 wines are very different, and I used some of the hard press to top up the 1st run wines, even as a 2nd run it had more body than the 1st run (not a lot, probably 1 bottle/carboy).
The medium press spent 10 months in a neutral barrel with 6 oz Hungarian oak (~3 months), while the hard press received no oak. The 2 wines are so different no one believes they are the same wine.
Two years from now it will be interesting to taste the 2019's and 2020's side-by-side to compare and contrast.