Arduino MEGA 2560 R3 only has 2 kb of RAM?

I have an Arduino UNO and needed more RAM for variables in my program, so I bought from AMAZON a NEW Arduino MEGA 2560 R3 that I just got. I loaded my program that I had on the UNO and it gives me the same error:

Sketch uses 28,714 bytes (89%) of program storage space. Maximum is 32,256 bytes.
Global variables use 2,239 bytes (109%) of dynamic memory, leaving -191 bytes for local variables. Maximum is 2,048 bytes.
processing.app.debug.RunnerException: Not enough memory; see http://www.arduino.cc/en/Guide/Troubleshooting#size for tips on reducing your footprint.

What the Heck!!!! I thought it was suppose to have 8 kb?

The package I received says it's from Mp3Car Store and was in a sealed box from Italy, so I'm assuming it came from the manufacturer. I can't find any numbers on the MEGA board, but on the box it came in has: X000J0EMPV and MD0147880 and says ARDUINO MEGA 2560 R3, and the board says ARDUINO MEGA 2560.

Did you select Mega as the board when you compiled?

no, i did not, had no idea, let me google that, thanks.

What's to google?
Tools:Board:Mega, verify code again.

who knows, very cryptic documentation.

Ok, finally got the memory issue resolved once I figured out what CrossRoads was saying, thanks by the way. Now I get the following:

Sketch uses 29,016 bytes (11%) of program storage space. Maximum is 253,952 bytes.
Global variables use 2,239 bytes (27%) of dynamic memory, leaving 5,953 bytes for local variables. Maximum is 8,192 bytes.

avrdude: stk500v2_setparm(): failed to set parameter 0x9e
avrdude: stk500v2_command(): unknown status 0xc8
avrdude: initialization failed, rc=-1
Double check connections and try again, or use -F to override
this check.

avrdude: stk500v2_command(): unknown status 0x01
avrdude: stk500v2_disable(): failed to leave programming mode