What grind size is best for espresso?

Sour, thin, fast: grind finer.
Bitter, dry, slow: grind coarser.

Fine, roughly 150 to 320 µm burr gap. On most grinders that's the finest third of the useful range. Check the chart for your grinder.

What grind size is best for pour-over?

Medium, roughly 560 to 850 µm burr gap, like coarse sand. Adjust by drawdown time and taste.

Coarse, roughly 850 to 1250 µm, like sea salt.

Settings on popular grinders

Grinder	Espresso	Moka pot	AeroPress	Pour-over / V60	French press	Cold brew
Comandante C40 clicks	10 to 15	15 to 20	14 to 24	22 to 32	25 to 34	30 to 40
Timemore C3 clicks	7 to 9	9 to 12	11 to 15	13 to 18	18 to 25	22 to 25
1Zpresso JX-Pro clicks from zero	1.2.0 to 1.6.0	2.4.0 to 2.8.0		3.2.0 to 4.2.0	4.2.0 to 5.0.0
1Zpresso K-Ultra dial numbers	2.2 to 2.5	4 to 5	4 to 6	6 to 9	8 to 10	10
Baratza Encore ESP dial	10 to 18	12 to 24	22	25 to 30	32	33 to 40
Baratza Encore ESP Pro dial	5 to 30		40 to 46	45 to 54	53 to 59
DF64 Gen 2 dial	5 to 17	17 to 25	25 to 40	40 to 55	55 to 65	65 to 90
Niche Zero dial	10 to 20	18 to 24	24 to 40	35 to 50
Fellow Ode Gen 2 dial		3	4	5 to 5.33	8	8 to 10
Fellow Opus dial	1 to 3		3 to 5	5 to 7	8 to 9	9 to 11
Mahlkönig X54 dial	1 to 5			15 to 25	25 to 32	30 to 35
Mahlkönig X64 SD dial	0 to 2			2 to 7	7 to 12
Baratza Vario / Vario+ macro setting	1 to 2	2 to 5	3	5 to 7	9

Each grinder counts differently, so compare within a row, not across rows. Sources for every number are on each grinder's page.

Method	Rough burr gap	What it looks like
Turkish	under 150 µm	Powder fine. It needs a grinder built for it.
Espresso	150 to 320 µm	Fine, like table salt pressed together.
Moka pot	320 to 450 µm	A touch coarser than espresso.
AeroPress	450 to 560 µm	Fine to medium, depending on the steep.
Pour-over	560 to 850 µm	Medium, like coarse sand.
French press	850 to 1250 µm	Coarse, like sea salt.
Cold brew	1250 µm and up	Very coarse.

Burr gap ranges overlap in practice and depend on the burrs, so use them as a guide.