The iMac is able to do both mirroring (show the same thing at the same resolution on both displays) or spanning (extend the desktop over both displays with each at its native resolutions (which can be different from each other).
I have a 20 inch iMac (1650x1080) connected to a 1920x1200 external and both run at those resolutions. I plan to get a 27 inch and run it with the 1920x1200 display.
If your MBP is switching resolutions when you plug in your tv go to system prefs/monitors and uncheck mirroring (or press the display mode switch function get (F7 on my MBP icon has two rectangles overlapped) to switch to running different resolutions on each display.