Furred dragons have become a wide range of creatures, and classifying them is vague at best, so this will be my subjective view.
My fursona Tiena recently had an identity crisis as I asked the important question What is a dragon?

The most common feature among furred dragons is the snout in the picture, which is usually similar to reptiles and the nostrils are on top of it. But not exclusively, but this is by far the most common trait. I believe that the only requirement for a furred dragon is to have fur or feathers.

Traditional dragons usually are mythological, and one or more of these features: breath attack, large size, wings, scales, whiskers, reptilian features, lays eggs, horns, etc.
There are also dragon types such as, Eastern, Eastern, Wyrm, Serpent, Wyvern, and so on.

Furred dragons don't have strict rules about what they are other than fuzzy dragons.
They may lack wings, have ears, be mammals, and require no supernatural abilities or relation to mythology. Which begs the question of whether they are dragons at all.
Although I have yet to see a furred dragon that doesn't have any draconic features, you may add that as the second required trait.
Of course a creator of their character can ignore the semantics and have any artistic freedom on what makes them a dragon. Not necessarily in a traditional sense.

Originally around 2018 my sona took inspiration from komodo dragons and maned wolves, then 1-2 years later I found about furred dragons, which shared many similarities due to the reptilian aspects. From that point on, I called my sona a furred dragon until now.

I concluded that my sona isn't an actual dragon, as his only dragon-like features are the snout and tail profile, but even those are based on komodo dragons.

So, I made a new species based on maned wolves and komodo dragons and I came up with the very original name feather maned dragon. But since the species is based on early real-life mammals, the name is a misnomer as he's not an actual dragon. Which is rather poetic, and this all comes back to a full circle.