relative clauses - Why is 猫 at the end of this sentence "目の色が違う 猫"

This sentence was translated as "a cat that has eyes of different color". Now using my Spanish speaking mind I wouldn't phrase that sentence that way, it would be 猫の目の色が違う.

So how come it is 目の色が違う猫?

Is the way I wrote it also valid, or it is syntactically wrong or unnatural?

Answer

目の色が違う猫

Here, Spanish is in an opposite order to Japanese. Where in Spanish you might say "Un gato con ojos de colores diferentes" (A cat with different colored eyes), Japanese normally places its adverbs, adjectives, and noun modifications before the noun. In a literal sense, think of this structure in this form:

目の色が違う猫
"eye's colors are different" cat
"el color de los ojos es diferente" gato

This is somewhat closer to English's construction of placing descriptions before nouns. If we change the descriptive sentence of 目の色が違う to something simple like 黒い, for example, this might make a bit more logical sense:

黒い猫 -> "black" cat (un gato negro)

白い猫 -> "white" cat (un gato blanco)
きれいな猫 -> "clean/pretty" cat (un gato limpio/bonito)

Japanese continues this sort of logical construction where in English it changes when adding verbs, using the "that" or "which" connection:

走っている猫 -> a cat which is running (un gato que corre)
寝ている猫 -> a cat that is sleeping (un gato que duerme)

... or using the "with" connection when talking about features:

尻尾が白い猫 -> a cat with a white tail (un gato con cola blanca)
目が青い猫 -> a cat with blue eyes (un gato con ojos azules)
目の色が違う猫 -> a cat with different colored eyes (un gato con ojos de colores diferentes)

EDIT: As for the other sentence structure you mentioned:

猫の目の色が違う

This is a simple, standard sentence. It means "The eye color of the cat is different/wrong/changed"

Let's parse both sentences to see why this is:

[ (目の色) が違う] 猫
[ (eye color) is different ] cat
[ (color de ojo) es diferente ] gato

This is describing the cat. The cat's eye colors are different (from one another).

[ 猫の (目の色) ] が違う
[ cat's (eye color) ] is different
[ del gato (color de ojo) ] es diferente

This is describing the difference. What is different? The cat's eye colors (not from one another, but from something else or a different time.)

EDIT 2: Added Spanish into the examples.