All my websites have built base on Wordpress cms but checking hosting offers, I saw web hosts are offering Wordpress hosting. My question is if I move my websites to Wordpress hosting plans, will they improve the speed and performance or what's the difference between Wordpress hosting and web hosting?
Unfortunately WordPress hosting has become a big debate, which it shouldn't have been. I will try to explain the difference without making it a page long post.
A small number of WordPress web hosts actually focus on just WordPress and only WordPress. Most of the staff may have been designers who worked exclusively with WordPress websites, and have done troubleshooting with just WordPress, so as soon as someone mentions an issues, the resolution is almost instant from previous experience.
Accounts are configured for just WordPress. Actual WordPress web hosts do not use cPanel, and will stay away Centos/Apache. Nothing wrong with them, but for WordPress, only two things are needed...PHP and MySqL. Control panels, one-click-installers, and the multiples of options available are not needed, which in essence become wasted use of RAM and resources.
Now without saying anything bad about other hosts...it's basically the comparison of taking an everyday family car to a Walmart equivalent mechanic, or taking a fine quality car to a mechanic that specializes in just that car. Perfect example...I had a nice car in high school (from my older brother) and there was specific mechanic he would go to that specialized in that type of car. The mechanic was about 30 minutes away. In school, 30 minutes was still a life time. So for an oil change, I decided to go to Canadian Tire. First and last time. After waiting 20 minutes during my lunch, the mechanic came to ask me where the oil filter was. Isn't that his job? Fortunately I knew where it was so could show him. A mechanic who knew that car would never ask that because it's their job. You pay a little more, but it's worth it.
The other differences...web hosts who sell WordPress as a marketing gimmick tend to sell just about anything hosting, and the packages are just a renaming of existing packages (Shared Package A -> WordPress Package A, Shared B -> WP B)...no differences between the two.
Again, it's not an insult to other hosts. Someone who is just starting to use WordPress or has a small amount of visitors....go with any reputable web host.
Someone whose WordPress website has a significant amount of traffic...is not interested in doing server management, and is making an income from their website would usually do well with a WordPress Managed web host.