The 20 year warranty may be prorated, meaning that if defects are found in the first year the manufacturer will pay 100% of the new liner cost only (not the installation), the second year they will pay 70% (or whatever) and so on.
20 years from now the manufacturer may only pay 15% of the new liner cost. Plus you have to prove the installation wasn't at fault, there was no negligence and lack of proper maintenance during the period.
What are considered defects? Probably just the seams. Discoloration, pattern mismatches and misalignments are probably not covered.
The warranty may also not be transferable (original customer only).
The discoloration you're seeing is normal: The anti-UV treatment that is applied to the PVC liner is more or less water soluble, after a few years it dissolves and leaves the liner unprotected. That part of the pool floor is more shallow and gets more UVs, the pattern eventually fades.
We observe similar discolorations up here in Canada, but with a distinct pattern: the lower half of the pool wall still has a pattern, the next few feet up are discolored, the remaining pool wall (above the water line) has a pattern. This is due to the fact we partly empty the pools come autumn so there's a few feet that are exposed to the sun. Of course the part above the water line still has its UV protection.