The TV screen reflects the screen shot on my Apple, but the TV program/movie does not show on the TV.
I assume this means you are physically plugging the MacBook into the TV (likely via HDMI) and the desktop picture appears on the TV while the SlingPlayer video output (in Safari, Firefox, or Chrome)) appears on the built-in MacBook LCD.
If that is true, either:
1) Drag the browser window to the TV "display" and set it to full-screen, if desired
2) Mirror the displays--see the discussion in Apple KBase article PH3793 about "Set up the displays for video mirroring"