What's the generic term for portable flashes (Speedlites, Speedlights etc) to distinguish them from studio strobes and alike? Is it simply speedlight/speedlite or has that just become a generic trademark (just like polaroid) due to Canon/Nikon being quite dominant in the field?
"Speedlight" is Nikon's brandname, and "Speedlite" is Canon's — but apparently Ricoh also used the name "Speedlite". That made me curious, and in a quick trademark search, it appears that no company has ever registered these terms, although an "American Speedlight Corporation" registered a letter-A-with-sunburst logo for their product ("Flash apparatus in which a capacitor is charged and thereafter discharged through a gas-filled tube to produce a flash of light").
That makes me suspect that the generic term actually predates any brand names, and indeed a Google Books search shows that it probably was generic before the current big brands' usage of it (even though these are old companies, their use of the word isn't ancient). The first reference I find is in National Geographic, from 1936 — but that turns out to be talking about Edgerton's work with actual high-speed strobe lighting, not the kind of portable flash you mean. After that, though, the term shows up quite consistantly in photo magazines starting around 1950, and clearly not in reference to any specific brand.
So, the history seems to make "speedlight" a pretty good generic choice, although (I think particularly because of pedantry about the Nikon/Canon loyalty divide) you might find yourself having to explain that you don't mean just Nikon. That suggests "speedlight-style" as a not completely unwieldy alternative less likely to provoke further need to explain — see for example "New Trigger Cable for Use with any Speedlight Style Flash". Or, you could use "speed light" with a space to distinguish from the brand.
Other options might include "hotshoe flash", which is fairly common, although when used with remote triggers (or via a cable) isn't necessarily completely accurate, as it might be a cold shoe. You could go with "shoe mount flash" and most people would know what you mean, but it sounds a little... awkward. B&H's "Speedlight Buyer’s Guide" also suggests "flashgun", and indeed that's also common (example: Digital Camera World; they use "flashgun" and "flash gun" inconsistently).
You'll also occasionally see the common style of flash called a "cobra flash", for the way it looks when bent to face forward. But, this is also sometimes used to refer to some pop-up flashes. And, not all hotshoe flashes follow this design, including budget non-tilt models, or — and here we are again pushing into the problem with "hotshoe flash", because another style is the "hammerhead flash", like the Metz mecablitz 45 CL, which is the same basic technology but meant to be attached to the camera via a bracket.
For completeness, Pentax just calls 'em "flash units" (even after the Ricoh acquisition), as does Metz; Sony and Olympus use "external flash units"; and Sigma seems to say "flashgun". But I still vote for "speedlight", "speed light", or "speedlight-style".
In the UK, "flash", without qualification, is often used to mean a portable unit. "Flash" is also used to refer to larger studio units. But, if the context doesn't make it clear which of the two are being referenced, or if there is a chance of confusion, then the prefixes "portable" and "studio" are used. This is the convention I'm tending to use.
You also hear "strobe" and "light" being used to refer to studio-flashes. Rarely is "strobe" used to mean portable-flash. The term "speed-light" (and variant spellings) isn't commonly used as a generic term.
The generic term is "electronic flash"... which, at the time it was initially used, served to differentiate it from bulb flashes, which could only be used one time per bulb. (Some bulb flashes had as many as ten bulbs in a single casing and would fire sequentially, but once you were done the ten, you threw away the entire flash unit.)
Of course, this is a bit of a long term so after the first mention, or if context is clear, you just call it a "flash" or "flash unit". "Speedlight"/"speedlite" are proprietary names for the same thing.
What's the generic term for portable flashes (Speedlites, Speedlights etc) to distinguish them from studio strobes and alike?
There kind of isn't one, since these days, there are also quite a few portable studio strobes, mostly powered by li-ion rechargeable battery packs, that have a lot of hotshoe flash features, such as TTL, HSS, and built-in radio remote control. I haven't seen a generic term come up for these types of flashes, either, aside from possibly barebulb flash, which doesn't even begin to encompass the battery-powered monolights like a Godox AD600 or Profoto B1X.
It's often implied that the term flash means a hotshoe flash, and that the term strobe means a studio monolight, but not always. And, of course, the only real distinction those two terms make is that the light throws out a short burst of light and is not a continuous light source; and strictly speaking, they are interchangeable.
Hotshoe flash, speedlight, and (in Europe) cobra flash are the terms I've seen most-often applied to battery-powered flashes you attach to a camera's hotshoe vs. lights that are designed solely for off-camera use.
Is it simply speedlight/speedlite or has that just become a generic trademark (just like polaroid) due to Canon/Nikon being quite dominant in the field?
Speedlight has become the kleenex of the hotshoe flash world. Speedlite tends to remain a brand-specific name for everyone who's not Nikon who wanted to avoid a lawsuit by not using "speedlight." :)