It seems to me that survival of the fittest refers to those who adapt to their environment and keep living while other species similar to them do not adapt, therefore the species does not survive.
No.
FIRST off, the mechanism that Darwin proposed, about adapting to the environment, is called “Natural Selection”, not “survival of the fittest”.
The “survival of the fittest” isn’t an evolutionary mechanism; it is merely description of what occur with Natural Selection, as Natural Selection explain how the ”changed“ environment can assert selective pressures to populations of species, that reproduce where they would have offspring/descendants with change/beneficial heritable traits.
Which would lead me to the 2nd point…
…SECOND.
What in the hell, do you mean by “keep living”?
Every organisms died...there are no exceptions. Were that simply poor choice of words?
…and, this following isn’t necessarily true, in all conditions…
No, it doesn’t mean species necessarily mean the species that don’t adapt, don’t survive. Those that don’t always mean that species will go extinct.
More often than not, it just mean that species diverged at certain points, with both species thriving in their given environments.
To give 2 examples.
Example 1;
During the warmer Pliocene epoch, parts of North America, Europe and Asia continents that were south of the Arctic Circle weren’t covered in ice sheets, so populations of brown bears lived much further north during the Pliocene, with no evidence of polar bears.
Then Pleistocene epoch came where these large regions of the continents periods that lasted tens to hundreds of thousands of years, that alternate through cycles of warm interglacial periods and colder glacial periods where regions were covered in ice sheets.
Some populations of brown bears continued to live in temperate regions, unaffected by ice sheets, so their physical traits have remained unchanged to this day These brown bears continued to hibernate during the cold winter seasons.
But those of populations of brown bears living in regions that now covered in deep ice sheets for ten or hundreds of thousands of years, would experience no spring to autumn seasons during their lifetime and lifetimes of their hundreds or even thousands of generations of descendants, can no longer hibernate as they usually do. Gradually, these brown bears evolved, eventually have distinctive physical traits that of today’s polar bears. These brown bears that adapted to the glacial regions evolved into polar bears.
The brown bears and their sister species, the polar bears, diverged at certain point during the Pleistocene, and continued to live in their respective environments during the Holocene epoch, with polar bears living in polar region, particularly at the Arctic Ocean.
Example 2:
Population of one tortoise species arrived in Galapagos from South America continent at some points in times and inhabited 19 islands. In most of these islands, they adapted to the islands with only minor changes, both large and small tortoises with dome-shaped shells. And in these islands, the highland, were humid, with vegetation low enough for them to reach and to feed upon.
but in couple of islands, the lowland islands were dryer and the more sparse vegetation were higher off the ground, so harder to reach. The selective pressures forced generations of tortoises to find mates with longer necks and longer legs, as well as growing shells that were saddle-shaped that allowed their legs to stretch to full height, and to let their necks crane upright.
The saddle-shelled tortoises are new sister species, living only in the fewer lowland islands.
The divergence of different species, don’t always lead to extinct of the parent species, so two or more species can co-exist at the same time in their respective environmental regions. So while your last sentence is only partially correct, “extinction” of species DO NOT ALWAYS occur for every cases and for every conditions, so you are also partially incorrect.
which lead me back to your “keep living”. Every individual organisms for some time, will die. Evolution isn about organisms dying, but about them REPRODUCING in changed environments with physical traits for survival for future generations of changed species.
stop thinking that “survival“ about “death”, but about the abilities to “REPRODUCE”.