It depends on your package, and you would need an HD STB. The Extreme HD will get all subscribed HD. Where Essentials package will only give you local HD. http://www22.verizon.com/Residential/FiOSTV/Plans/Plans.htm
Does anyone know why for certain stations I get the normal non-HD station (like MLB tv, Versus, Speed, etc.), but I do not get the same stations in HD. If I get them in normal TV shouldn't I get the same stations in HD especially because I have an HD plan with many other HD stations.
If you receive "many other HD stations" other than the local networks, then it sounds to me like you're on the old FiOS TV Premiere package.
Verizon created a new package called "Extreme HD" that added 10-15 new HD channels such as Versus, Speed, Fox News HD, FX HD, and ESPNews HD. If you want these new channels, you've got to upgrade.
The Extreme HD package costs $57.99/mo by itself, or you can get it in a bundle with 20/5 Internet for $79.99/mo (plus any STBs or DVRs) when you commit to at least one year of service. This is called the "Flex Bundle" or "Flex Double Play."