OK, this is a pretty involved question....
The term "remi" or "remy" applies to human hair; the rest of the terms you mentioned apply to synth. What remi, or remy, means is the source of tons of debate. In my opinion, the term may have at one time meant that the hair was cuticle-intact or single-drawn, but now it's morphed into a vauge marketing term that sellers use liberally to describe what they consider to be high-quality hair. And of course, what's high-quality is debatable, too.
Here's my understanding of the different grades of synth:
WaWa qualifies as thermofiber, as does Ebonyline Adore, Freetress Futura, American Dream thermo, and OPH (organic protein hair). These are all suitable for loose extensions. Thermo is more heat-resistant than other synth and therefore won't fry if you use a curling iron or flatiron on it when the hair's wet. It takes a while to curl, in my experience (because of that resistance), although I believe the time may vary from brand to brand. The therms are relatively new to the scene, but are getting good reviews so far. They seem to hold some curl after washing, although it loosens. The biggest problem seems to be a lack of color and length choice and limited availability (I imagine we'll be seeing a lot more of this hair in the next year, though). I'm not sure that therm would work for heat-sealed extensions, but they'd be suitable for everything else.
Monofiber/monofilament has been around forever and includes Dome, PlastikHaar, Trimco, and ProStyles/ProHair. It's high-quality synth that's suitable for loose extensions. You can use steam and hot rollers as much as you want on dry hair, as well as a curling iron or flatiron when the hair is wet, but you do need to be careful with metal tools (doing test strands, etc.) or you'll fry the hair. It seems to hold some curl after washing, although it loosens, too.
To my knowledge, those two are the best for loose extensions because they'll stay relatively soft, silky, and tangle-free. I believe kanekalon is a more general term that can apply to high-quality monofiber/monofilament, like PH, or lower-quality stuff like kanekalon silky braid. Either way, it's important to look at the brand.
Toyokalon, polypropylene, or jumbo braid are a definite step down in quality from the others. They may be good for falls--and I think they work quite well for dreads--but for loose extensions, you'd want to stick with thermofiber or monofiber/monofilament.
:)
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