You've got it right with the options thing. I've never traded the US, but I guess if they are 100 shares per contract, then your calculations would be correct.
There are 2 basic types of call spreads. The bull call spread, and the bear call spread.
Bull call spread involves buying a call, then selling a call further out (higher strike) to offset the cost of the bought call. As far as being long, the one you bought is the long "leg" of the spread, as you have gone long a call. The higher strike call is the one you have gone short on.
So, in spread trading you are both long and short. Long and short refer to whether you have bought or sold an option. In spreads, you do both.
In the bear call spread, you go short (sell) the call, then go long (buy) the call with a higher strike for protection. Again, you're still long and short, just switched around based on your directional view.
Hope that explains it.