From what volts does it regarded as the high voltage which needs extra care and probes and devices in measurements?
I don't think there is a one answer fits all. It will depend on what you are trying to measure and what equipment you are using.
For example, I have a UNI-T UT90A that can read I think can read close to 2KV before it over ranges. I think Dave's 121 over ranges around 600V. I personally wouldn't put these meters across a 600V high energy bus but I have certainly demonstrated them running with low energy sources.