Are people, who are working on physical fitness, exercisers?

Here are a couple of options. I think that they apply to most of the people in your category, with the possible exception of people in physical therapy.

• Gym bunny

• Fitness enthusiast

• Exercise buff

• Fitness fanatic

• Health nut

My personal choice out of those 5 options would probably be gym bunny, fitness fanatic, or fitness enthusiast. They all represent people who exercise often as the sole meaning. Health nut is also good but has the side meaning of eating healthy so using it would depend on the context. Exercise buff is fine but implies that the person is muscular - which they may not be. This is not to say that exerciser doesn't work - I think that it may still be one of your best options regardless of personal preference on the sound of the word.

Even though it's not used often, mover is a fine word, which means what it sounds like (a person or thing in motion), but I fear there's a deeper reason there's a struggle to find an "-er" word to describe this kind of being: agent nouns tend to describe agents who do the activity in an ongoing way.

For example, a runner is not merely someone who can run or who did so only yesterday, but someone who does so regularly. A painter is someone who is at least partially defined by their propensity to paint, not just someone who needs to touch up a wall that got damaged.

In the same way, the loose collection of "beings that move their body" will probably always resist an "-er" label because it includes beings that have differing levels of attachment to the regularity/proficiency of their physical activity.

To my ear, an "exerciser" is someone who is defined by their activism around a specific right, like that of free speech in many countries.