So whenever we are afraid or anxious and we feel that thing in our bellies, is it the brain sending messages to the belly or the belly reacting and sending messages to the brain?
If we're in a grounded, reflected and self-connected place (i.e. if we have empathy or warm accompaniment from ourselves or someone else), we can interrupt this cycle. The signal "the gut is tight" from the gut can be discerned "ah, interesting, I wonder if it needs to be tight or if I should change the topic or watch a different movie or leave this room", etc.,
Here's an example: You see a tiger in the forest. Your eyes send that signal through their nerves to the brainstem, which makes your stomach tight and activates your legs to run away. The tight stomach and running legs then send their signals of movement and clenching back up through to limbic system ("I'm scared!") and the neocortex (your conscious brain, "I'm running away from the tiger!") to tell it to run. Because all of this happens so fast, our experience is this: We saw the tiger and therefore we're scared and are running away. That's not really what's happening under the hood, we're scared BECAUSE we're running and have a tight gut, the tiger was just a trigger for the brainstem/gut/legs. Makes sense?
Emotional states aren't reified in the brain; they're reified in our physiology. When you're happy, or sad, or scared, or whatever else, that's not a fact about your brain; your brain is just perceiving a fact about your body. (A fact that it worked together with the body to create, but still.)
Think of the brain as the CPU and the body (muscular contraction levels, etc.) as RAM. The brain-as-CPU has registers (informational state held directly in the brain), but your emotions are not held directly in such registers. Emotional states are, instead, patterns of information in the body-as-RAM, that the brain-as-CPU (statelessly) perceives [loads from, polls] in an ongoing way. If the body-as-RAM is polled and shows a certain recognizable pattern of activations, then that is interpreted by the brain as a certain emotional state.
Both the brain-as-CPU and various body parts (devices on the bus) can write to the body-as-RAM. The brain-as-CPU will then notice that the "emotional state" that it reads from the body-as-RAM has changed, and may do something about it (reinforce the change, counteract it, etc.)
What you experience as the qualia of emotion, is the brain's perception of the body-as-RAM, the same one it uses to decide whether to "do something about it."