I answered this in another forum and thought it would be helpful to pass along here too.
WordPress hosting - Marketing Gimmick. Usually just a shared account renamed as a WordPress package. Also usually on a cPanel host and offered through a one-click option, alongside emails, dns, add-on's, and 250+ other scripts that can be installed in the same account.
Customer - someone starting out or has low traffic.
Managed WordPress Hosting - An actual WordPress host. Usually not using cPanel or any panel. Has an optimized setup that doesn't use Apache, and has staff trained in server management and WordPress. No emails, dns, or anything else not needed for WordPress.
Customer - someone who relies on their website and may have moderate to high traffic.
Fully Managed WordPress Hosting - Word play and the same as Managed..although we all know for some, managed just means they reboot and tell the customer it's online, or they actually cover everything.
When I see these debates, it reminds me of an older import car I had in high school from my brother. It wasn't fancy, but it also wasn't one of the common domestic cars. I had a mechanic that my brother sent me to who would only work on those make of car. One time I needed an oil change I figured I would go to the Canadian Tire 5 minutes from my school since my mechanic was a 45 minute drive away. After the car was on the hoist for 20 or 30 minutes, the guy came to ask me where the filter was. Luckily I knew and showed him. My mechanic wouldn't need to ask such questions.
Same story relates to hosting;
Send a ticket to the common "any host can host WordPress" and go back and forth with responses for hours, to only be told to get your own help. Or go with a host that specializes in WordPress and have the issue resolved from the initial ticket.
Also some will factor in price and say it's too much. A client who knows and understands business will never think this way. If their hosting cost them $1200 a year, they're the type of client that could afford to pay this and will sleep well at night knowing that $1200 expense helped them make $90,000. Or even if they pay monthly, that $100 a month expense helped them make $2000 that month. A smart business person understands their time, and knows that the $5 a month host will cost them $200,000 of lost income, or that $100 will let them sleep at night.
Another thought when it comes to price...If a $100 a month expense is too much, then imagine those who run a business where just the monthly lease is $2000 before any other expenses are factored including the cost of starting that business.
I haven't made a music business analogy in a while, but a true WordPress Host (or Managed) are like music artists that make music for the love of music. Such host were doing just WordPress before it became cool. The artists you hear on the radio everyday making the garbage music...those are the WordPress hosts that do it for marketing. Theses hosts pay affiliate sites to fool the public, like record labels pay dj's and radio stations to make a song #1 over night.