|Question1. No difference, different name, same thing.|
Question 2. That depends. Not all computers,have a graphics card. The graphics hardware is often built into the motherboard. This applies to nearly all laptops and and some low end motherboards.
You can usually tell of the graphics hardware, either a card or built in, is not working properly when you get a blank or distorted screen. However, a blank screen can also be a symptom of other problems so without more details it is impossible to say.
The inability to install a game can be down to a whole raft of problems from incompatibility, lack of disk space, lack of memory, faulty memory, the list is endless. So without some symptoms it is impossible to say.
Diagnosing computers problems is usually a process of elimination, working out what it isn't so all you are left with is what it is.