If you go to a doctor you know a few things about their background: they have a college degree, an advanced degree, have passed exams both oral and written to be licensed, have a number of years of training beyond their medical school, (first an internship and then residency... which differ... a surgeon may be a resident seven years, a dermatologist two or three), and that after their training they will be required to re license and take continuing education as long as they practice.
There are quite a number of professionals with whom one may work in fitness, and the scope of practice (what services and information they should be giving you based on their training), as well as the training and licensure differ greatly for different types of fitness professionals.
You can think of fitness as an adjunct of your basic health care. One form of health care is treatment oriented: you get sick, or have a condition, and you see a physician, who either offers treatment or refers you to a specialist (another physician or even a physical therapist, or other health care provider). Another form is preventative: you see your physician regularly and receive information and referrals to maintain health, rather than to cure disease. Some people do not start with a GP (general practitioner physician), but with a nurse practitioner, or a Naturopath, or some other alternative. But whatever it is that person is kind of the person at the door who helps direct you to the path you need. There are quite a lot of professionals involved in the 'health care' (both curative and preventative) to which at one time or another you may go: physical therapists, occupational therapists, speech therapists, rehab specialists, psychotherapists, behavioral therapists, addiction specialists.... etc.
Within the area of fitness there are also a ton of different kinds of professionals, and a fair amount of overlap of scope of practice.
I am a yoga teacher. I teach yoga. I do this in groups large and small, and with individuals. I do not have a specialty certification for yoga with kids, so I do not teach those classes. Some yoga teachers have special training with yoga therapy, to work with people with specific injuries or conditions. Most yoga teachers will have a designation on the Yoga Alliance: an ERYT 500 will be highly trained and have taught several thousand hours, an RYT 200 will be registered and have completed a 200 hour training program, for example. There are some very senior teachers who will not have an Alliance status. I know of one teacher who trained with legendary teachers in India decades ago and does not have Alliance status. But for most teachers this is a way to tell you have a teacher with a basic amount of training. Yoga is not regulated in the way that, say, massage therapy is, so this self regulation is very helpful.
Yoga is one of the mind body disciplines. These are disciplines that stress the connections of mental and physical functioning. Those who train in, and teach yoga also often work with yoga based or other meditation techniques, relaxation training, and stress management.
I used to be a personal trainer. The scope of practice for a trainer is all forms of physical exercise. Some trainers have additional training in senior fitness, or children's fitness, or sport conditioning, or post rehab, etc. They can generally do fitness testing and assessment, create fitness programs, and work individually with you on those programs.
For that I carried a special certification which required extensive study. There is a thing like the Alliance that began recently to try to be a clearing house for trainer certifications. It is really necessary. In years gone by a trainer often was someone who worked out at the gym and had a 'good body' and would get hired to help others 'pump up'. These days most trainers have a certification and many have a degree in a fitness related field. But certifications vary, so it is helpful to know which are nationally recognized. There is a big difference between hiring someone who did an online open book test where they could look up the answers, and someone who has had a proctored exam (someone watching and timing the test). And trainers are not really regulated either, so there is an element of caveat emptor. Look for a NCCA accredited certification (I know, I know, before the AFAA people write in, that does not have NCCA but is respected), ACE, ACSM, and NASM are some of the best known.
What I am not is a nutritionist. A nutritionist has a degree in nutrition, and is licensed. A nutritionist can assess diet, provide meal plans, and so on. This is similar to stress management and yoga. I am not a therapist. I do not do therapy. I do however, understand the principles and practices of the discipline of yoga as they relate to stress release, and mindfulness.
Nutritional counselling is a hot topic right now. As fitness professionals of all types, and personal trainers in particular, have become more educated, and research driven, there has come the realization that exercise is only part of the equation. Without addressing the 'what goes in' part of the equation the 'what gets used' part of the equation will not lead fully to a healthful or fit place. This could have led personal trainers to go back to school en masse for degrees in nutrition, or could have led to trainers and nutritionists creating webs of aligned services. Some of this has happened. But what has also happened is that some trainers are pushing the boundaries of their scope of practice in some cases. A trainer generally has to have some familiarity with fitness nutrition to be certified. However, while a trainer can provide basic information of the place of food in the equation, they may not make meal plans for you. And selling supplements without a nutritional or medical background is not ideal.
We are also seeing a new category of fitness professional: the life coach. The life coach should have a broader mission than the trainer, and in addition to a trainers background, additional training in nutrition, motivation, stress management, and so on. This is a way to recognize how helpful it is to work with one person who has an understanding of a multiplicity of aspects of wellness. If you hire a life coach do be aware that it is a relatively new category, and as usual, look for a nationally recognized organization for certification, and also for whatever other trainings, skills, and certifications the person may have.
There are a lot of other types of professionals one may work with in fitness/health. My favorite is the massage therapist. But you might work with a person trained in Ayurveda, or Pilates, or Zumba, or other types of group exercise, or MELT (myofascial release), or a coach for a particular sport..... When you work with someone in the field the basic questions you would ask remain the same: what certification do you have? Is it nationally recognized and/or NCCA accredited? How long have you been teaching/training? Do you have a degree that relates to your field? If the field requires are you properly licensed? What services do you offer (and do they fall into their appropriate scope of practice).
The range of what members of the community of fitness professionals have to offer is as varied as is the community they serve. Even within categories there is a huge range of background and training. One trainer to another, one nutritionist to another, one yoga teacher to another, can be as different in their approach as a trainer to a yoga teacher, or a massage therapist to an occupational therapist. Every time I get to work with someone new I feel like I learn so much. But I always try to work with those whose commitment to their field and to their clients is expressed in their commitment to their training and study.