Chaturanga is called a push up as short cut to help students understand but it’s different.
Ideally the hands are flat and the wrists are below the elbows, that’s why the elbows are in close to the body. Key muscles in the upper back and chest are used to flow through the position as you glide off the feet lifting up and opening across the chest to upward dog.
I agree there’s no right or wrong but there is safe and unsafe. Flowing through chaturanga mindlessly can damage the shoulders over time. While doing push ups in training, there’s typically more focus on alignment.