The electromagnetic spectrum charts are cool and all, but in reference to the original question, I assume the context was what law enforcement/EMS/local government refer to as "High Band."
Typically, the 150 - 160 MHz range (in VHF-High) is what most agencies refer to as High Band. The Illinois State Police refer to this range as either "High Band" or "HFn" where "n" equals a channel number (HF1, HF4, etc.). This would of course never be confused with "HF" in the radio spectrum which refers to the 3 to 30 MHz segment. ISP refers to VHF-Low frequencies as Low Band or LFn, but they're still in the VHF segment.
Of course, on an agency-by-agency basis you never can guess what their nomenclature is. A police department where most of their comms are at 460 MHz might refer a frequency at 155 MHz as Low Band or LF, just because the frequency is in a lower band. I know of one PD that calls their car-to-car simplex channel "Band 2" even though their "Band 1" repeater is in the same band, along with the repeater input.