Fine lines and wrinkles are not the same thing
The two words get used as though they were interchangeable, and the difference between them is the difference between something a serum can visibly affect and something it cannot.
A fine line
Shallow, and it sits in the surface. It shows most when skin is dry and tight, and it is often noticeably less obvious on a morning after a good night with well hydrated skin. It moves with the condition of the surface, which is why the same line can look different from one day to the next.
A wrinkle
Set into the skin rather than sitting on it, from years of the same expression and the structural change underneath. It looks broadly the same whether your skin is well hydrated or not, and no surface product is going to take it out.
Why the distinction is worth having
It tells you which claims are plausible before you read the price. A hydrating serum making a fine line look softer is ordinary and believable. The same serum promising to remove a set wrinkle is promising something a surface product cannot do.
What to expect, said plainly
Well hydrated skin looks fuller and reads smoother overall, and fine lines are the part of that most likely to look different to you. Set wrinkles will still be there. Anybody telling you otherwise is either mistaken or hoping you do not check.