I think the proper term is circumstellar habitable zone. If there is other life out there, why are we assuming that it’ll have the same basic needs as our animals? The universe is seemingly infinite, and there’s endless possibilities of what’s out there, so why do we only consider planets that are the ‘perfect’ distance away from their star?
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We aren’t assuming life will absolutely, definitely have the same properties as life on Earth, it’s just that we know what Earth-like life does, so we have a much better idea of what to look for. With a countless number of planets to search, it only makes sense to start with the ones where we have the highest chance of noticing any life that does exist.
That being said, chemistry works the same across the universe, so we can make some pretty good generalisations about what life needs, particularly in terms of temperature and radiation. Too much radiation anywhere makes any molecule that forms too unstable to be able to form life, because life, whatever molecules it uses, requires a degree of stability.
As for temperature – life is really just a bunch of chemical reactions happening in order. Too cold, and those reactions happen too slowly to be coordinated. If it could count as life at all, we couldn’t detect it because it would act over such long timespans that it didn’t look like life. Even colder and the solvent – the liquid that these molecules move in, which for Earth life is water – freezes solid. If molecules can’t move, they can’t react, so a cold planet can’t sustain life. Too hot and there’s so much energy that the complex molecules necessary for life break down into smaller things and just whizz about accomplishing nothing. This means there’s a minimum and maximum temperature that life can exist between, which is broader than the goldilocks zone we currently consider, but still exists.
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