Spell-check is no help here and neither is context, because both words turn up in the same professional register — legal writing, consulting, technical documentation. "A discrete enquiry" and "a discreet enquiry" are both plausible phrases with completely different meanings, and only one of them is what you meant.
An adjective meaning careful, tactful, unobtrusive — not drawing attention.
An adjective meaning individually separate and distinct.
Discreet and discrete come from the same Latin word, meaning separated or distinguished, and they are pronounced the same. They split into two unrelated meanings.
Discreet means careful and tactful, especially about keeping things private or not drawing attention: a discreet inquiry, a discreet earpiece, be discreet about the news. Discrete means separate and distinct: the project has three discrete phases, discrete data in statistics, discrete components in electronics.
The spelling carries its own reminder. In discrete, the letter t sits between the two e's and keeps them separate, which is exactly what discrete means. In discreet, the two e's sit quietly together, keeping a secret.
Please be discrete about the reorganization until it's announced.
✓Please be discreet about the reorganization until it's announced.
This means keep it quiet: discreet.
The rollout happens in four discreet stages.
✓The rollout happens in four discrete stages.
The stages are separate and distinct: discrete.
She wore a small, discrete hearing aid.
✓She wore a small, discreet hearing aid.
Unobtrusive, not drawing attention, is discreet.
Quick way to remember
Look at where the "e"s sit. In "discrete," the two "e"s are separated by a "t" — and the word means separate. In "discreet," they sit together, keeping quiet side by side.
What are the nouns?
Discretion comes from discreet: "use your discretion", "at the manager's discretion". The noun for discrete, discreteness, is rarely used outside mathematics.
What does "discrete data" mean?
Data that can take only separate values, usually counts, such as the number of customers. It contrasts with continuous data, such as height or temperature.