VPS plans are similar to shared plans in that both feature multiple websites hosted on a single server. However, VPS plans maintain a strict separation between clients and websites when it comes to resource allocations. Your site gets its share, and no one else may use your resources (conversely, you may not cannibalize the resources allocated to others' websites either).
WordPress is one of the most popular content management systems (CMS) in the world, and as such, many web hosting providers offer options that cater to this rather large niche. You can certainly host your WordPress site on a standard shared hosting plan, but by choosing a WordPress-specific option, you'll spend less time configuring and managing your WordPress installation.
Many services offer a low "starting price," but require you to prepay for two or three years of service to get that price. After the promotional period, the renewal price for some services can be two, three, or even four times the initial promotional pricing. While the initial deal might be incredible, the cost of transferring your site (or paying the added fee) in a couple of years may be something to consider.