OK... so here's a total rewrite. "Professional work experience" is, in my mind, any paid work that relates to your profession. Internships count, although I would expect shades of grey here where your intership is so tied and controlled by the academic institution that it is really "hands on coursework" and not a paid short term learning engagement. For me at least, the line of demarcation is in how much time you spent being part of the team in the company you worked in - in some cases, internships are almost entirely divorced from course credit, it's just a simple final peice of paperwork to receive whatever recognition is requied by the school. In others, the "internship" includes professorial mentoring, close monitoring by the academic institution and as much time spend satisfying coursework requirements as the needs of the company - in those cases, I'd call it coursework, not "professional work experience".
Longetivity plays a factor here. I doubt anyone can give a hard and fast rule, but when you're within 3 years of your internships, you may want to call them out separately, specifically as internships. When you're further on in your career, that extra year of half a year is not a big factor.
Here's some examples of how I answered this question during the course of my career. I worked summer internships at the same company after my 2nd and 3rd years, and then the company paid me for part time telecommuting while I finished my degree on campus. I hired on into a corporate program which I did for a year, and then placed into a permanent assignment which I held another 2 years before my division was sold to another company:
Just graduating - "I worked X company, doing two summer internships, they then paid me part time my senior year to keep me on the team". Form entry: 1 year - internship - X company
1 year after graduation - "I've been working full time for a year, but I've worked with the company through a few internships before that, so I've been around for 3 years" Form entry: 2 years - FTE & intern - X company -- or-- one line item for FTE work, one line item for each internship.
5 years after graduation - "I'd been with X and Y companies for a total of 7 years - it's a long story, but it was a collection of internships, corporate programs, and then a sale of my division." Form entry: 4 years - various positions - X company, 2 years - position name - Y company (the purchasing company)".
8+ years after graduation - "This is what I'm up to now..." it has to be one heck of a good conversation if we're going back to the ancient past that is my internship, probably a long conversation with an old acquantaince with a shared history. Form entry: 4 years - final position - X company, 3 years - final position - Y company, more years - more positions - more companies"
14 years after graduation - I actually had to go look at my own resume to remember when I started that internship and the years at company X and company Y just so I could fill out another form. Given that the 2 years of interning are now a small fraction of my professional work history, I don't see it being a big deal one way or the other - with intership, I've worked 16 years, without 14 years - either way I'm a lifer who's worked about 15 years.
In every case, if asked for a single, raw number, I'd just sum it up and include the internships. In the cusp of around 5 years, there seems to be a transition for most people where the work on internships is decidedly less important or worth highlighting in almost any venue when compared to the work done more recently. For the most part, people reading forms are more looking to place you in a bucket. I'm sure the buckets vary from place to place, but a common example is 05, 5-10, 10-20, 20+ Once they figure out which bucket, most form-requiring systems move on to the next question. If you are at the dividing line between buckets (9 years, but with internships, its 10 or 11) then you can figure that they will look at other parts of your data anyway.