Strobes and flashes such as on-camera speedlights are largely battery-powered while monolights must typically be powered through an AC or DC source like a battery pack or outlet. Most monolights also include a modeling light for previewing the lighting setup and effects you’re creating in a scene.
With monolights, output is generally offered in watt-seconds (W/s), a measure of the maximum amount of power capable of being generated each second (equivalent to joules). While manufacturers often use the W/s as a gauge for the power of a monolight, these numbers should be considered a general rule of thumb because total light output can be affected by numerous other factors, including the design of the light and any light-modification tools used like reflectors.
Very inexpensive base models, often best as secondary solutions for multiple light setups or optically triggered "slave" units, start at roughly 100W/s. For a primary monolight with enough power to light a basic scene on its own, you should start at 300W/s or more. Professional systems begin at 1200W/s or more.
Remember that quality of light can matter as much as power. Higher-end systems can often be matched in output and specs, but top-of-the-line systems from pro companies like Profoto and Broncolor typically offer much better color rendering and more consistent light output from burst to burst, as well as very fast recycling times and durable, light-efficient builds. More affordable systems will often vary slightly by each burst with color shifting as the bulb ages, and even between pops or when adjusting power.
Intermediate systems are quite capable, however, because more power isn’t always better. Changing the distance of your monolight to your subject can be as effective as adjusting the power. This means that lower-rated lights can still provide a lot of illumination when situated close to your subject, while higher-rated lights can be too powerful to achieve a shallow depth of field even at the lowest setting, especially when the distance to your subject is limited in a studio situation.
Depending on your needs, it may be beneficial to purchase multiple mid-tier or low-tier lights over a single expensive pro model. When combined, multiple lights add to your light output exponentially at the same time that they give you much more versatile lighting setups.