Luster and lustre both describe a gentle shine, or figuratively, glory and distinction. Luster is the American spelling, lustre the British one, so the choice comes down to your audience rather than the meaning. Think of it like centre and center: same word, different side of the Atlantic.
The core difference
The two spellings are regional variants of one word, not distinct terms.
- luster — American spelling, for a soft shine or added prestige: The necklace had lost its luster after years in a drawer.
- lustre — British spelling of the same word: The award added new lustre to her career.
How to tell them apart
Both forms come from Middle French lustre, ultimately from the Latin lustro, meaning to purify or to brighten. The word can also work as a verb, as in silverware that lustered under candlelight, though the noun sense (a shine, or figurative glory) is far more common.
Writers most often trip on this one when switching between US and UK style guides mid-project, or when a spell-checker set to the wrong region quietly "corrects" one spelling into the other. Setting your document's language to en-US or en-GB before you start avoids the inconsistency.