Why is a 'wish' different from a 'desire'?

I've seen two possible answers for this, both of which I like.

You wish for something unlikely or nearly impossible. Whereas you desire something that's more achievable or attainable. So a wish is more passive than desire, which you can more easily act upon.

The other is that there is a difference in the intensity of the longing. Desire is something more intense than a wish, which is more of a "wouldn't be nice if..." as opposed to, the "let's make this happen" of a desire.

I'm afraid that this is somewhat subjective, and depending on how you use them they could conceivably mean close to the same things, but that's connotation for the two words.

The differences are subtle, a wish is wanting something to be true while a desire is a yearning or longing for something and is generally more emotional.

Desire vs. Wish
What's the Difference?
Desire and wish are both expressions of longing or wanting something. However, there is a subtle difference between the two. Desire typically refers to a strong feeling or craving for something, often accompanied by a sense of passion or intensity. It implies a deep yearning or longing that is driven by personal needs or wants. On the other hand, a wish is more of a hopeful or optimistic expression of wanting something to happen or be true. It often involves a sense of imagination or fantasy, and may not necessarily be grounded in reality. While desire is rooted in personal desires and motivations, a wish is often more whimsical or dream-like in nature.

https://thisvsthat.io/desire-vs-wish

When you wish upon a star
Makes no difference who you are
Anything your heart desires
Will come to you