I would probably consider it much closer to a spin-off than a unique entity. Its many unique concepts are completely overshadowed by the fact that they have too many characters and gameplay features in common with the mainline Mario series. They're 2D platformers wherein you collect the same coins as you do in the Mario series, fighting many familiar enemies such as Shy Guys, eventually culminating in a climatic confrontation with (Baby) Bowser. Multiple games in the series--including but not limited to the very first entry--feature (baby versions of) Mario and Luigi as prominent figures in the story and lore. The unique settings and environments added, not to mention experimentation with art style, do allow it to stand out from the series it spawned from, but unless you have been living under a rock for 30 years (or aren't familiar with Mario lore), there's virtually nothing you can do to separate Yoshi from his roots as a Mario character within the internal logic of the games themselves.
By contrast, Donkey Kong may be connected to Mario in a similar fashion, but the setting, characters, enemies, game assets, art style, and story of the Donkey Kong Country games are all so completely removed from anything related to the mainline Mario games (or even the Donkey Kong arcade games that spawned them) that it would be much harder to actually connect them together than it would be to separate them. Aside from being 2D platformers where you collect something equivalent (but distinctly different) to Mario coins, the two share absolutely nothing in common.
Even if Yoshi's games were as completely devoid of Mario iconography as the Donkey Kong Country games are, Yoshi himself is far too prominent a figure in the mainline Mario games, often serving as a playable companion in many of the games, making it impossible to view him as a completely separate entity, whereas when Donkey Kong does appear, it's usually for spin-off games (Mario Party, Mario Kart, etc.) or for roles that aren't terribly important.
I might be inclined to compare it to... well, honestly every single comic book character ever, really. Characters like Robin, Nightwing, Harley Quinn, and others may all have their own separate books with their own separate stories, but no one is buying an issue of Robin without the immediate knowledge that he's the sidekick of Batman and the contextual expectation that his background will play some role in where the story goes. Whereas one might read an issue of Superman and feel comfortable completely separating it from other comics by the same publisher, even though every comic I've mentioned in this sentence share the same universe and continuity.
So while both Yoshi and Donkey Kong do share a similar amount of grey area and both have their roots in Mario, Yoshi wears it far too much on his sleeve and is far too active in the actual mainline Mario games to justify categorizing it as a completely separate series.
