Getting Mario-Mask Koopas in “Super Mario World”

There is a secret warp in the Star Road. Upon entering it, you will end up in the Special World. If you complete all 8 of the Special World levels, a new Star Road appears with a warp that leads back to Yoshi's House. If you enter it, some drastic changes occur in Dinosaur Land:

• World backgrounds change (to a Fall-like instead of a Spring-like colour scheme).
• Koopas transform into Mask Koopas.
• Piranha Plants will change into Pumpkin Plants.
• Jumping Piranha Plants will turn into Jumping Pumpkin Plants.
• Bullet Bills are replaced with Pidgits.
• Goombas turn into a yellowish color and have sunglasses. (GBA version only)
• Pokeys turn into sawblade-like creatures. (GBA version only)

(Source: Super Mario Wiki)

These changes occur in the entire world, and are permanent.

After beating the final Star Road level, "Funky", a second star-road teleporter will appear to the left of the level. Taking this teleporter will send you all the way back to Yoshi's home back in world 1, and will simultaneously activate the "Special World".

Here's a picture to explain how to avoid triggering the Special World: