Standard resolution is 160 x 192 x 4 but pallet tricks allow for most games to use 16 colors at a time. A few games actually use 256 colors. The high res mode is 320 x 192 x 3 (black and 2 shades of 1 color) and does not allow pallet tricks. However, cross-color artifacting can be utilized in high res mode to produce up to 9 pseudo colors (black and 4 colors with 4 shades each). However, this only works reliably on standard NTSC CRT televisions that were not designed to take advantage of composite input; other types of monitors (and most emulators) will usually show the picture in black and white.
Multiple resolutions can exist on different areas of the same screen. This allows for use of low color high res areas of the screen with other standard resolution areas in 256 colors. Use of 320 x 192 and any number of colors qualifies for the hires tag. Note that the Atari 5200 also has a 40 x 24 text mode (8 x 8 characters) left over from its Computer roots.