Let me see if I can put some thoughts in perspective. First some definitions as I have seen them. These are my interpretations based on experiences over the years.
The Hobbyist:
Someone who has other means of Income, enjoys playing music for others, views the Sound Equipment as "big boys toys" and really does not care about DJing to make a profit. That person almost always would not declare any incomes derived, to the IRS. That person also likes to be in the Spotlight as center of attention at a party.
The Part Timer:
Someone who has another means of income but nevertheless views DJing as an additional means of income. They may as well as they may not declare that income to the IRS. They take what they do seriously.
The Full Time Business DJ AKA the "Professional":
Trust me, if one DJs for a living and has been doing so for a long time they are truly Professional in that regard. The full timer does not only work when they are at a Gig but are also involved in Marketing their business, honing their skills, etc. That is time consuming. Looks, such as wires/no wires showing at a gig really is not a measure of professionalism as much as knowing what to do and how to please a crowd. The looks are more of a cosmetic aspect.
There are other elements which can apply to any of the above three categories.These elements can help the public to form an opinion of the person presenting themselves as a DJ.
Presentation of oneself and their gear (The way one dresses and the condition of their gear)
The equipment chosen for the task (How does it sound, adequate, inadequate, like a stereo on steroids or full bodied to replicate a band)
Pricing: The Full timer is astutely aware of the balances between expenses, investments and profit margin to bring about enough money on which he/she can make a living. They treat what they do with respect and in all seriousness so there could be an expected result.
True professionalism in the business can come from the experiences gained over a period of years. Knowledge of marketing, selling, delivery of a stellar service, knowing and understanding their gear and respecting the Industry. When one calls themselves a DJ, the public then tends to judge all in the industry by certain standards.
Clients who are classy would expect classy.
Clients who don't care would not have high expectations of the DJ as long as they play music.
When all is said and done, each person has to look in the mirror and truly define themselves. One can fool some of the people some of the times, most of the people most of the times but not all the people all the time. Lastly, at no time can one ever fool themselves, they just pretend.