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A match is essentially a piece of wood, while a lighter is a mechanical device. So it's easy to assume that the match was invented first. But this wasn't actually the case.
In 1823, a German chemist named Johann Wolfgang Dobereiner created what was known as “Dobereiner’s Lamp.” The early lighter was a jar-like container. When one turned the valve on the top, hydrogen was released and catalyzed by zinc metal in the jar, causing a flame.
Matches, on the other hand, weren't invented until three years later, in 1826. The first matches weren't very successful however, and it wasn't until they started being coated in (toxic) white phosphorus that they really took off. (And we do mean took off – often these matches would ignite on their own.)
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