What is the difference between the flash and continuous lighting, why not using continuous lighting for photography?

A flash light is small, portable, and usually battery operated. In order to minimize battery drain, the duration of illumination is electronically controlled, typically between about: 5ms ( 5 thousandths of a second); and 50μs (50 millionths of a second).

This allows, for example, four fairly cheap AA sized alkaline batteries to provide typically between 100 and 1500 flashes, before the batteries need to be replaced (or recharged if using e.g. Ni-MH batteries) - giving many months of usage for a typical amateur photographer.

Continuous illumination studio lights typically provide around 600W of illumination (often with a lot of heat dissipation as well) which would require a current of 100 Amps to be drawn from a 6V battery source (comparable energy source to that fitted in an electronic flash) thus completely draining the batteries in under one minute’s usage - IF small batteries were to be used. For this reason, continuous studio lighting is normally electrical mains operated.

The heat dissipation resulting from multiple source studio lighting may cause the ambient temperature to rise to uncomfortable levels, particularly in a small studio, or in the confined spaces typically used for still-life macro photography.

Some electronic flashes can be zoomed in step with a zoom lens, thus concentrating all the available light onto the subject at ranges up to around 100 metres - e.g. for long range night-time wildlife photography. Illumination intensity decreases with distance according to an “inverse square law”, thus, a 600W (non-zoomable) studio light that provided adequate illumination at a range of 3 metres, would require 100 times as many lamps to produce the same amount of illumination at 30 meters (60 kW); or 900 times as many (over half a megawatt) to illuminate a subject at a range of 90 meters - a range that I can spot-illuminate adequately with just one of my electronic flashes.

Some night-photography is best achieved by using a long time-exposure (slow shutter speed), to get adequate “exposure” from things like street-lights, candle flames, stars, etc., combined with a short duration flash to provide adequate illumination of foreground subjects e.g. a face - that would otherwise just appear like a silhouette. Such techniques are just not possible with continuous lighting unless somehow using “double exposures” (which are perhaps ok with older film cameras, but not with modern digital cameras)

….. or by using “photoshopping” techniques.

The main (and possibly only) advantage of continuous studio lighting: is the ability to make precise adjustments to the illumination highlights, shadows and hues, in order to get the exact, aesthetically most pleasing, image that one intends to achieve.

The link below shows some nice examples of night flash photography that just could not be achieved with continuous studio type lighting.