I don't think many people can understand your question, so let me answer it for you.

Fitness coach is the general name of fitness industry. Many people don't know that fitness coaches generally include several kinds of jobs, such as personal trainers, group gymnastics coaches and bodybuilding coaches.

The title of fitness instructor is generally called by people outside the fitness industry. If you only talk about a fitness instructor, you can't clearly express what this person does.

For example, "fitness instructor" is equal to the word "driver", but drivers are also divided into bus drivers, bus drivers and truck drivers, which are essentially different.

I hope my answer can help you.