ISBN and ASIN are both identifiers, but they are not the same thing. One is a global publishing identifier, the other is Amazon's own internal catalogue identifier.
ISBN is a recognised book identifier used across the publishing industry.
ASIN is Amazon's internal product identifier used inside its own marketplace.
If you only think about Amazon, an ASIN may seem enough. But if you want your book treated like a normal commercially distributed title, ISBNs still matter.
That is why many authors use official ISBNs even when Amazon also assigns an ASIN.
ASIN is Amazon-specific. ISBN is industry-wide.
If you want a stronger publishing setup, wider compatibility, and a recognised identifier beyond Amazon, ISBN is the one that matters most.