Hi Katy,
The answer to your question is that Managed WordPress Hosting could be either a shared account or a vps. The term “Managed” in Managed WordPress Hosting generally only means that your hosting provider is going to help you managed certain parts of your WordPress site.
For example, if you don’t use the best backup plugin we know, Total Upkeep (a BoldGrid plugin!), to backup your WordPress site, your managed hosting account may help you manage backups by doing them for you automatically.
You can follow these links to learn more about Managed WordPress Hosting and WordPress VPS Hosting.
DreamHost and InMotion Hosting offer managed hosting accounts that you may want to check out as well.
Let us know if you have any further questions!
– Brad