Sealed means they let a walrus pee on it.
Sorry. Seriously, it means some kind of thin glue has been smeared across the primer, water-sealing the edge of the primer. Traditionally it's red-tinted so you can see it, although clear fingernail polish will work just fine.
"Hardcast" means a plain lead bullet was made harder, either by alloying it with a harder metal in the lead such as tin or antimony or dropping it from the mold while still hot into a bucket of water to quench it. The goal is a harder bullet that won't deform and will avoid leading the barrel at higher speeds.
A softcast bullet is typically OK at 1,000fps or below, sometimes less (900fps fr'instance). Hardcasts can be pushed harder, 1,400fps or higher.
Another way to prevent leading is a "gas check" - a copper base-plate below the lead bullet. It only extends up the "sides" of the bullet a couple of millimeters at most, and doesn't add to the bullet's total width. It's kind of an "extreme mini-jacket" that prevents the burning powder from burning the tail end lead off the bullet (which is a major cause of plating the inside of the barrel with lead). This can allow you to push a softcast (defense oriented, usually) bullet faster than you otherwise could.
Hardcast bullets are generally either used in rifles (where they're going to go too fast no matter what you do so that softcast would smear their way down the barrel) or for hunting or critter-defense loads.
Hard or soft, plain lead bullets (or at most, gas checked) have an advantage over jacketed: lead is slicker than copper (or brass) and therefore you get more bullet speed for less pressure than jacketed. That's why a lot of top-end hunting loads for big-bore handguns and rifles (such as 45-70) are hardcast, to maximize both bullet energy and "deep punch" effects. Study Garrett's site for more details:
http://www.garrettcartridges.com/products.asp