In real world biology, serum is the clear yellowish fluid left over from blood when you separate out the blood cells, normally by spinning in a centrifuge. It can still contain antibodies among other things, but no red cells.
In recent decades the word has also been misappropriated by elements of the cosmetics industry for use in describing some of their products to give a veneer of scientific authority to them.
there is also something called truth serum
Neither pentathol nor any other drugs with similar effects are a serum in the proper scientific use or definition of the word, despite often being colloquially referred to as a truth serum.
What does the term 'serum' refer to in science fiction stories?
In science fiction it pretty much means whatever the author wants it to (or thinks it does).
In my experience it most often means an injection that bestows long term (or permanent) physical / physiological advantage or improvement of some sort. The "super soldier" serum that made Steve Rogers into Captain America is a prime example.
Their effects often bear closer resemblance to something that might be achieved with gene therapy than anything a real serum can do and take instant or near instant effect from a single injection. This in no way is meant to suggest there is anything remotely realistic about some (or even any?) of their effects, simply that a closer ("closer", not "close") real world analogue for them would often be gene therapy rather than the word serum that is most often used for them.
But the effect of a "serum" in science fiction can be anything, so really it defies any definitive definition other than simply saying that it's any sort of handwavium that bestows powers or effects if injected.
Google: serum meaning
Cambridge Dictionary : Serum
Quora : serum in biology