Most likely, the Teke Teke story isn't real. It's likely a creation passed down to add a bit of spookiness and thrill. Such stories often have elements of exaggeration and imagination.
The main key element is the girl who was cut in half by a train. Her form of moving around on hands and elbows and making the 'teke teke' sound is also important.
Well, the Teke Teke full story is quite chilling. The origin of this legend might be related to the fear of railway accidents and the unknown. People often fear the idea of a dismembered spirit seeking revenge. In Japanese horror culture, such stories are used to evoke a sense of dread. The image of a half - body entity moving around with a strange 'teke teke' sound is both terrifying and has captured the imagination of many, not just in Japan but also around the world who are interested in Japanese horror stories.
The significance could be that it represents a unique sad story in an English - related context. Maybe it's a story that stands out among others in terms of its sadness.
The phrase 'la triste historia in english the only story' is quite puzzling. 'La triste historia' is Spanish for 'the sad story'. The 'in english the only story' part seems out of place or perhaps it was an attempt to say that there is a sad story which is the only story when translated into English. It could be that there is a collection of stories in Spanish and this one sad story is the only one being considered for an English version or something along those lines. Without more information, it's difficult to be more precise.
I'm sorry, I'm not familiar with the specific 'la mujer del vendaval full story'. Maybe you can provide more context or look for it in relevant literature or online resources.