> There is no mechanism in the body to turn fat stores into muscle.

Which is why you can’t build muscle without eating, but you can have a calorie deficit building muscle from food consumed and losing a greater mass of fat than the muscle built. “Convert fat to muscle”, I will admit, was a perhaps overly informal description of that for this context, but its the net effect.

Not true! There’s the indirect mechanism you might be referring to when you say “both can be used for energy”: adipose tissue releases triglycerides, liver extracts glucose from triglycerides, muscle tissue stores glucose as glycogen. And there is also a direct mechanism - adipose tissue releases triglycerides which are directly stored in muscle tissue. This intramyocellular triglyceride is concentrated in skeletal muscle tissue and plays a significant role in endurance exertion (https://pubmed.ncbi.nlm.nih.gov/14987125/).