The native vertical resolution is always 480 scan lines for NTSC channels, analog and digital. There are still the 480 scan lines per pair of interlaced fields (= 1 frame) but how much detail is preserved on each scan line (horizontal resolution) may vary from one channel to another even on the same cable system. I don't know what Time Warner does.
Most cable TV systems use compression to fit more channels on the cable. Compression often shows up as the inability to preserve the narrowest details on each scan line.
Numbers for comparison: For VHS tape, typically the smallest detail as preserved can be about 1/300'th the screen width; for standard NTSC broadcasts, 1/400'th; for DVD, 1/700'th (1/720'th for some).
Video hints:
http://members.aol.com/ajaynejr/video.htm