Depending on where you live or which brands you use, there is a different terminology for “studio light“
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Studio Flash Light/ Strobe Lighting /Studio Strobe /Monolight
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Is there a difference between monolight and studio strobe? 
The terminology is similar, but a monolight and a studio strobe are not identical.
In common usage, a “strobe“ most typically means a monolight, just as “flash” most typically means a speedlight.
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WHAT IS THE DIFFERENCE BETWEEN STUDIO STROBE/MONOLIGHT AND A SPEEDLIGHT?
Speedlight: A speedlight is a small battery-powered flash that is usually mounted on the camera. It can also work not mounted as OCF (off the camera flash) with an umbrella or softbox. 
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Strobe and Monolight:
A strobe or flash is any light source that fires a brief burst of light, vs. being a continuous light.
A studio light which has an integrated unit that contains both the power supply and the flash head is known as a “monolight.” That makes it very portable and useful both inside and outside of a studio.
So a monolight is a type of strobe, just as a speedlight is. It is a self-contained studio flash which allows the attachment of light modifiers such as a soft box or umbrella. It consists of a power source and a light head, which is all contained within a single compact housing.
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Which Brand?
I often get asked for brands. If you can, best is to actually go to a photography store and look at the different brands and see which ones you like.
Brands for studio lights: for example Godox/Westcott/ Elinchrom
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I personally could not work anymore without a studio light. It has allowed me to grow and scale my photography business as well as it helps me to optimize my post production workflow substantially when it comes to saving time. 
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You don’t need your own photo studio. Most studio light kits are very easily foldable and transportable. I do ALL my photo shoots with mobile studio lights at the clients location!!
When you have a dream, you’ve got to grab it and never let go. 
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