In the US, if you say 'strobe' or 'speedlight', they will assume you're talking about a hotshoe flash. If you say studio strobe, they assume you're talking about monoblocs.
In the UK, and most of the rest of the world, if you say 'strobe', they will think you're talking abut the stroboscopic special effects light unit seen in discos. The kind that emits very short bursts of light on and off very rapidly for the 'freeze-stop motion' effect. Your SBs of EXs or studio monoblocs - those are actually called 'flash'.
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Kenji, which modifier to use depends on several factors. Primarily, what sort of control one requires for a certain look or effect.
The main consideration is not whether you're shooting outdoors or indoors, even though that has some bearing if bounce and reflected light is a criteria, as well as environmental considerations, aka, strong winds etc.
Most photographers just getting into off-shoe work (I hesitate to say 'Strobing') or studio flash will probably experiment with either a softbox or an umbrella.
There's a lot more to artificial light control than just a softbox or umbrella, but those are affordable and fairly easy to start with. In capable hands, those two modifiers could probably cover 50% - 75% of a photographer's needs ... depending on what kind of photography you do, and what lighting styles and techniques you prefer.
BTW, no need to worry or get scared by all the different modifiers you see. Just think of it this way - simply, they help diffuse light, reflect light or concentrate/restrict light. If you take time to study the basics, learning how to see and control light becomes easier.
CHEERS!
