There are some exceptions to this rule, such as providers that started with shared hosting and have since added managed hosting, but in general you can only host wordpress sites on a managed WordPress provider. Technically, all you need is the latest version of PHP and MySQL, which are typical features of any web host running Linux. You can find some shared wordpress hosts that offer even more WordPress-specific features, but the above are pretty much the base standard. Of the three options above, it might seem like a no-brainer that you should go with managed WordPress hosting, but there is one type of hosting service that falls between managed and DIY.
Hosting your WordPress site on a VPS can work well if you're passionate about servers and have the time to do it all yourself, but if you're not technical or are trying to run a business, managed hosting is probably a better solution. With wordpress hosting you get resources and tools specifically designed to help you get the most out of your WordPress website. With managed WordPress hosting, you'll find a huge benefit in the fact that your entire technology stack is tailored to the WordPress experience. This type of hosting is also cheaper overall, although the price difference may not be significant for shared plans.
Many of the managed WordPress hosting providers include support in case your site is hacked and have systems in place to protect you from malware. On the other hand, standard web hosting gives you more control over all aspects of your website, which can be an essential factor for more experienced users. Eventually, you will be ready to take the next step and host a slightly higher risk site, such as a client's brochure site. While the cost may be higher than the shared hosting plans you're used to, I can promise you that you'll get much more value from managed hosting.