The distinction being made when we talk about "understanding" and "choices" I about the distinction between sentience and sapience.

Dogs are sentient, meaning they have a conscious experience involving emotions and works with memory and instincts to determine motivated actions. This is a complex system that results in complex behaviour like preferring one food over another, stubbornly ignoring your commands, or recognizing when you're upset and coming up to you to comfort you. It's beautiful.

Sapience is related to the capacity to be meta/self-aware. This is what is normally meant by "understand" and "choice" when talking about how "special" humans are. As far as we can tell in experiments, dogs do not have the capacity to understand themselves like "I'm a dog who really enjoys walking" or "Good dogs take care of people, so I'm going to choose to take extra care of human because I want to be good." This is what you might call "wisdom" or "rational" behaviour, and some animals to exhibit sapience to an extent. Both can be involve what we think of as "choices" e.g. selecting one of several options, but they're distinct behaviours.

Humans engage in both, making it extra confusing. I'm not being particularly meta-aware and rational when I choose to cut off a piece of my steak and eat it. I am being more meta-aware when I choose to slow down my eating because I want to be respectful of my friend who cooked it for me, and I want to savour the moment, appreciating the flavours, texture, and effort that went into its preparation.

My dog knows that I prepare her food and she expresses her emotions and desires to me and she responds to my behaviour/communication. But she doesn't understand that I chose to rescue her or that we are two people living our short and shorter lives together.