Use leach when a substance is filtered out by liquid passing through something, such as nutrients leaching from soil in heavy rain. Use leech for the blood-sucking creature, or for a person who takes advantage of others without giving anything back: he's such a leech, always borrowing money he never repays.
The core difference
Leach is about liquid drawing a substance out; leech is the worm, or a person who freeloads.
- leach — to remove a substance by letting liquid filter through it: Heavy rain can leach nutrients out of the soil.
- leech — a blood-sucking worm that lives in water: A leech attached itself to his leg while wading through the pond.
- leech (figurative) — a person who takes advantage of others: He's such a leech, always borrowing money he never repays.
How to tell them apart
A handy hook: leech is the one with a job title attached, in medicine as well as in everyday complaint, since leech is also an old word for a physician, from the days when doctors reached for leeches as standard treatment. Keep that image of a doctor's tool in mind and the creature spelling follows. Leach has no such double life; it only ever describes liquid drawing a substance out of something, as chemicals leach out of soil.
The mix-up shows up most in environmental or gardening writing, where people meaning to describe chemicals leaching into groundwater instead reach for leech, borrowing the more familiar creature's spelling by mistake.