Where DK sits
The Craft Yarn Council lists DK and light worsted in category 3, Light. It sits between category 2 Fine and category 4 Medium. These categories contain ranges of yarns, not one fixed diameter.
When substituting
A familiar name on two labels does not promise the same fabric. Compare lengths, fiber and construction, then make a washed gauge swatch. The yarn substitution calculator compares the length required and whole skeins to buy; it does not decide whether the yarn will suit the pattern.