Mould and mold are the same words spelled two ways: mould is the British spelling, mold the American one, and both cover the fungal growth, the shaping container, and the verb meaning to shape. Remember it by country, not by meaning: British English always adds the "u".
The core difference
Mould and mold cover exactly the same meanings, from fungus to shaping container to the verb to shape; the only difference is British versus American spelling.
- mould — British spelling for the fungal growth, the shaping container, and the verb to shape: Green mould had spread across the bread overnight.
- mold — American spelling for the same three senses: Green mold had spread across the old loaf of bread.
How to tell them apart
The shaping sense of "mold"/"mould" (the container and the verb to shape) comes from Old French modle, itself from Latin modulus, reaching English via Middle English molde. The fungus sense is a separate word historically, tracing back to an Old English root connected to soil; it has simply merged into the same spelling over time.
The confusion turns up most in cookery and cleaning content: a British recipe tells you to pour batter into a cake mould and to check the fridge for mould, while the American version of the same text uses mold for both. Whichever spelling you choose, keep it consistent across fungus, container and verb within the same piece of writing.