ok, i'll bite
hard cast simply has to do with the materials used to contruct the bullet. it means it has less lead content and more hardner in ratio. soft lead is usually 1/ 20 parts lead.
gas checks are a copper cap attatched to the base of the bullet. purpose: two.
one, keeps the powder gases away from the bullet base and usually utilized in magnum type loadings with lots of hot gases.
two. also cleans the barrel of lead deposits to prevent build up of further lead deposits and spreads open to seal the barrel.
and thats about as much as i know. and i'm as simple as can be