The word "strobe" is a bit abused for still photography as "strobe"
comes from "stroboscope" which means to flash regularly over time.

There are 3 general types of photographic flash in common use today.

1. Studio strobe pack lighting
   These have a "pack" (or pak) that has the capcitor bank and charging
mechanism.  The photographer sets the power, typically in 1 stops steps
for each (or pairs) strobe light (head) connected to the pack.  Some
packs have 3 or 4 channels of output where 2 channels output one set
amount of power and 1 or 2 other channels output another set amount of
power (individually or as a fraction of the other channel.

The camera triggers the pack to fire (via PC sync, on camera flash slave
detector or wireless device like a pocket wizard (in the PC sync circuit
on both camera and pack)).  The actual lights are at the end of a cord.
 These are typically the most powerful and fastest recycling strobe
systems.  Advantages also include a single pack for all the controls and
connections; single point to adjust power to the flash heads; ratio
controls on the pack, etc.
    Disadvantages include high weight and some danger if working around
wet areas.

2. Monolights
   Most of the features of a pack in a head assembly.  One light only,
of course.
   Advantage: lower weight, portability.
   Disadvantages: need several to light a scene.  Need to assure that
they all fired.  Usually a relatively low power level overall compared
to packs, but you usually setup at least 2 - 3 units in any case so
total power may be about the same.

Both pak systems and monolights typically have an incandescent modeling
light built in (75 - 150 W typical).

Both pak and monolights are total discharge systems: the photog sets the
power and the caps are charged to a level to match that "setting".  When
triggered, the caps are completely discharged.
(vice AUTO/TTL/E-TTL/Pre-flash where the flash is fully charged and the
power to the light is interrupted when the correct amount of light has
been output to the light with a very fast switch called a thyristor).

3. On camera flash.
   manual, automatic, TTL, E-TTL, etc. as commonly found for 35mm (and
other) cameras

Cheers,
Alan

 A mono-light typically refers to a stand alone flash. No aux power
pack. The unit can be plug into wall current or some have battery packs
internal- or closely connected. The downside is they generally cost more
money and then you have to find two outlets instead of one. The upside
is you don't have to have long cords connecting them to a central power
pack.

Strobe as Alan states is a rather generic term & can apply to a
mono-light as well

   Monolight, as I recall is a brand name.   Strobe is a name for a
repeating source of light, often misused to identify an electronic camera
flash.