Both have hints of existence in life, however what is the difference? One is made up and want to have as (Fantasy) and the other is in the technology uncovered by Science or other lobotomy (Science Fiction). Is there a deeper representation of where the line is drawn between these 2 genres which sometimes even mesh and join forces, or is it just a vague idea in the minds about their distinctive properties?
The most traditional division between science fiction and fantasy (Which, admittedly can be blurred), is that for science fiction it is something that is based in reality and might be possible. Fantasy is not grounded in reality, so is not possible.
So, despite Arthur C. Clarke's 3rd law - "Any sufficiently advanced technology is indistinguishable from magic", if it is based in rules of reality, current scientific knowledge, it will be classified as science fiction. There are also "divisions" in science fiction, such as soft and hard sci fi. Soft science fiction is more concerned with characters and society, hard science fiction places a much greater emphasis on being based in actual science.
There are also divisions in fantasy, such as low and high fantasy. Low fantasy is based in our world with magical elements (Terry Brooks Shannara series), High fantasy is based in an alternate/made up world (Tolkein 'verse).
Two points: First, SF can't be "fiction based on the possible" because as far as we know, 99% (at least) of what people think is SF is not possible.
Second, it's not possible to neatly divide fantastic fiction into "Fantasy" and "SF" since much of it obviously is a bit of both.
So, a better way to talk about it is to say:
A story is SF to the extent that it depends on fictionalized science or engineering, where "science" is understood to be any systematic, rational body of knowledge about objective reality.
A story is Fantasy to the extent that it depends on fictionalized magic or the supernatural.
Note that what makes a story SF, for instance, is that it depends on a fictionalized science. If it's just a mundane Western where the Bad Guys have blasters, then it's not really SF at all.
Likewise, a story that depends on real science for its impact -- the movie Apollo 13 for instance, isn't SF either, though many readers of SF still loved it.
And stories can be simultaneously SF and Fantasy when, for instance, magic is treated as a science in the stories (e.g., Randall Garret's Lord Darcy stories of de Camp and Pratt's Enchanter series.)