The larger or more complex a website, the more comprehensive a configuration package it's going to need. The main ones are broken down as follows:
Shared web hosting is the basic package that services offer. Your website sits on the same server along with many other websites, so you're sharing the server, and any other resources, such as memory or CPU. These are good for basic website needs such as email sending, file sharing, and base level ecommerce sites. Shared hosting is the cheapest and therefore smartest option for smaller or startup businesses.
A virtual private server is designated for your direct purposes, more than a shared server. You still may be sharing an actual server, but the service creates a virtual server of your very own. That means all the resources are yours alone, from memory storage to processing power and beyond. This is a safer and much more reliable option that keeps your site separate from the others while still maintaining affordability.
Dedicated hosting is already another level. In addition to getting your own server, dedicated hosting lets you take full control over your server. That means you have full administrative access and can set things up the way you like it. This type of package comes with a royal suite of features that may not be necessary for all types of businesses.
WordPress is a shared hosting service that caters to a more specialized clientele. The servers themselves are optimized differently, and have features that are particularly attractive to WordPress performance such as faster load time, pre-installation, security features that work specifically with WordPress, and WordPress updates. This is useful for businesses that have websites created on WordPress.