Mario is a big series.
There are a few sub-series, and six questions on this site are on the donkey-kong tag. Of those six, five are about the Donkey Kong Country series of games.
Donkey Kong the character, along with Cranky, Funky, and Diddy Kong, is clearly part of the Mario universe; Donkey Kong's father (now Cranky Kong) was first in Donkey Kong as the villain who is fought by Jumpman, an old name for Mario. Now, he appears in almost all spin-off Mario games, and Diddy Kong is frequently in them, too. However, I don't know if the Donkey Kong Country games are part of the Mario universe. I cannot think of any connections outside of characters.
Should these questions have the super-mario-brothers tag?