People have been scrimping and saving for centuries, but whether they’ve also been skimping and saving is a more nuanced question. “Scrimp” and “skimp” are closely related, and some speakers may even use them interchangeably. However, they still manage to suggest different attitudes toward money and necessity.
“Scrimp” is the older of the two, dating back to at least the late 1600s. It originally described something that was scant or meager. For example, if you have a scrimp understanding of something, that means you don’t understand it very well.
Later, “scrimp” could be used as both an adverb and a verb. The verb refers to restricting expenses or being frugal. This is where we get expressions like “scrimping and saving.” By the 1800s, “scrimp” could also be used as a noun to describe something small or inadequate, such as “a scrimp of a nightie.” It also picked up noun and adjective forms, including “scrimpy,” which could describe a parsimonious person or something that's meager.
“Skimp" may actually have come from “scrimp,” though we don't know for sure. It comes into the language first as adjective in the 1700s, with “skimpy” following in the 1800s. It was used to describe something that’s lacking, such as “a skimpy bathing suit” or “a skimpy budget.”
Today, “skimp” is more common, but “scrimp” is still out there, and some people use the words interchangeably. For people who do make a distinction though, it has a lot to do with perspective: Frugal saving vs. stingy spending.