An effect saying 'Wild Mongrel gets +1/+1 and becomes the color of your choice' constitutes which two types of effects?

The correct understanding is that the effect stating "Wild Mongrel gets +1/+1 and becomes the color of your choice" can indeed be categorized as both a power-and-toughness-changing effect and a color-changing effect.

When an effect gives a creature a bonus to both its power and toughness, it modifies the numeric attributes that determine how much damage it deals and how much it can take before being destroyed. In this case, the "+1/+1" clearly indicates a boost to both power and toughness.

Simultaneously, the phrase "becomes the color of your choice" involves a change in the color identity of the creature. Color-changing effects typically result in the creature being affected with characteristics of the new color(s). Therefore, this effect simultaneously alters the color of Wild Mongrel while enhancing its combat potential.

This alignment with the definitions of power-and-toughness-changing and color-changing effects substantiates why this answer is correct. The other options, while they may reference alterations in various forms, do not encapsulate the full scope of changes taking place as described in the question.