Manufacturers of digital cameras sell multiple product lines, each targeting a particular corner of the market. These can be divided into consumer, prosumer or professional categories. The most obvious initial difference lies in cost.
A point-and-shoot camera with its built-in lens can be significantly less expensive than a camera system that allows you to swap lenses and use accessories such as a removable flash unit. Most people (including many photographers) would argue that a $300 camera is "better" than a professional system costing several thousands of dollars. But what does that really mean?
A professional camera, at the most basic level, is a camera used by a photographer to earn a living. Major camera makers would have you believe that you need this year's camera model and painfully expensive, pro-grade lenses to produce quality work. So it might surprise you to learn that there are skilled photographers today using entry-level, "obsolete" cameras to create salable works of art.
Cultivating an eye for composition, paying attention to how light interacts with the subject, and skillful post-processing all matter more than the camera. For proof of that, see this article about a woman who creates fantastic images using an old point-and-shoot Canon! There are many stories about people using older gear to make amazing photos, including many who still shoot, or have returned to using, film cameras. See here and here, for proof.
Professional photographers know how to work within limitations, and will even use those shortcomings to their creative advantage. Unconventional and beautiful portraits have been created using 50mm or shorter lenses that are not typically regarded as suitable for the purpose. In my own experience, some of my most compelling work has been made using inexpensive, "toy" film cameras. Cheap, plastic cameras like the humble Holga or the mysterious but marvelous Debonair may look like mere toys. In my hands, they are professional cameras.
Some cameras are admittedly less suited for specific uses than more technically advanced cameras. I love shooting with my Debonair, but I'm not going to grab it to shoot a soccer game. Its fixed shutter speed and wide lens wouldn't work well to capture action on the field. It's simply not the right tool for the job. Sometimes you really do need a long lens, increased low light sensitivity, super fast shutters and other features found on more expensive cameras.
Professional DSLRs generally feature more physical dials and buttons for adjusting exposure than cheaper consumer models that require diving into menus to access the same settings. This ease of making rapid changes is important to professionals who need to make many adjustments over the course of shooting a wedding, for example, adjusting to changing lighting and the desired effect for each photo. While they could make do with an entry-level DSLR in a pinch, it would be less convenient than using a "pro" camera. It's important to note here that image quality isn't at issue.
The end product, the photograph, is vastly more important than the tools used to create it. Print an 8x10 from a pro and consumer camera, place them side by side, and almost nobody will be able to tell which camera made which photo. Megapixels don't play as big a role as people suppose: an 8x10 print of a photo made from my old Nikon D40 (6 MP) will produce the same pleasing results as the same size print from a modern 24 MP camera. The advantages of having many more megapixels are normally not apparent until you print at sizes that most people never use.
Now that mirrorless cameras have been adopted by many photographers, I don't run into much criticism of my Fujifilm digital cameras. On occasion, however, I've had people turn up their noses because they don't think my gear looks as professional as a Nikon or Canon DSLR. (Sometimes the brand name "Fujifilm" leads people to mistakenly confuse them for a vintage film camera.) In short, it's not what many people visualize when they think about professional gear.
I chose my current system for a variety of reasons, after months of careful research, and I know from regular practice exactly how these cameras will perform in my hands. I can achieve the same photographic results with my cameras that I would using a much bulkier camera.
Mirrorless cameras come with the normal ratio of benefits to drawbacks, just like every camera system ever made. If there were a universally agreed-upon perfect camera system, the other makes and models would quickly be out of business as photographers flocked en masse to buy into it. As much as photographers tend to be fanboys or fangirls of our chosen system, in the final analysis all cameras are just boxes with holes in them that gather light. It's up to the operator to make something memorable with them.
People sometimes ask me what kind of camera they should buy. The answer is that it really depends. It depends on how much money you have to spend, how much complexity you can adjust to using, what features are most critical to you, personal aesthetics, your physical tolerance for gear of varying weights, and the kinds of stuff you plan to photograph. I can tell you that my camera suits my style and feels like an extension of my arm and my eyes. Not everyone has the exact same needs.
In the end, every camera I own - from $20 thrift store buys to my latest Fujifilm X-T2 - is, or at least has the potential to be, a professional camera. If a client is looking to hire me, it's because they like the work I've done. The camera I bring to their special event is only a small part of the equation.