scrimmage

Scrimmage is a corruption of skirmish — the sounds got worn down and reshaped over time until a new spelling took hold.

The facts here don't trace a documented shift in meaning, only that the word's form drifted away from its source, skirmish, until it stood as its own distinct word.

Because scrimmage comes from skirmish, the two words are directly linked — one is essentially a shape-shifted version of the other.