The differences are a ton and below are just the basic info. I'll let you guess which one is which (private trader, retail trader and professional trader)...
Trader A - Licensed, stable salary, performance bonus, regulated, most likely did an internship prior to being hired, in house training after being hired, compliant department ensures they follow the rules, college educated, low failure rate, job includes health/dental insurance with other benefits (e.g. stock shares) and that includes psychological help if needed...
Trader B - Not licensed, unstable salary, high failure rate, no performance bonus, not regulated, most likely did not do an internship, no compliant department (trader relies solely on himself/herself), does not need to be college educated, high failure rate, pays for private health/dental insurance and usually does not include psychological help if needed, a lot tougher to get loans to buy a car or house...
Trader C - Former professional trader that quit the job to trade their own account. Usually has 1 - 3 employees and is still connected to the professional network.
Simply, there's a huge difference. Seriously, I'm from a trading family and I'm the only retail trader in the family. My old man worked on the floor when I was a kid and I currently have three relatives working for firms (BNP Parabis, Credit Suisse and Société Générale) plus friends of the family working for professional firms.
There's a huge difference between retail, private and professional. Its possible the confusion here is that some retail traders call themselves a professional trader if they're profitable and trading for a living. In reality, that can only happen if the retail trader treats his/her trading like a business and has most likely setup their taxes in which they pay themselves a salary so that their personal income is different from their business income for tax/liability reasons.
As for prop traders, I really don't personally know any. Thus, I don't know what they call themselves nor do I know how their government view their occupation for tax reasons. That's the other issue, depending upon what country you're being taxed in...the distinction may be a little more blurred between the groups or LESS blurred.
The way I see it, its not really about what you call yourself. Its more about what you can do or get with that title. It starts with if you're trading for a living as your primary source of income and then you can go into the other stuff about how you're setup your trading for taxation and how you've setup your bank accounts and so on.
My point is that the government, insurance companies and banks or other organizations know exactly what you are regardless if you agree with them or not. Therefore, if you're a retail trader and you literally treat your trading like a business...you're a professional in the eyes of those organizations because you're in the business of trading.
So yeah, there clearly are differences and I'm very comfortable with those differences considering I made a choice right out of college to go retail instead of working for a firm as a professional trader. There's no shame in calling yourself retail and if someone works for you...you can even call yourself "private trader" (hint). The latter is a phrase more common in Europe and Asia.