I think you've correctly picked up on the difference between "uniquely" and "infeasable".
It's not possible to use a hash function to give every possible input a unique reference. But a cryptographic hash function aims to make the inputs to "hash collisions" be very different. So, for real world files the hash is unique, because the file that would produce a hash collision would be malformed and useless.
In general when you hash a message you don't want an attacker to make subtle changes and get the same hash.
"Here is my electronic payment for £100" should never have the same hash as "Here is my electronic payment for £10,000. Nice to meet you on the weekend".
I think you've correctly picked up on the difference between "uniquely" and "infeasable".
It's not possible to use a hash function to give every possible input a unique reference. But a cryptographic hash function aims to make the inputs to "hash collisions" be very different. So, for real world files the hash is unique, because the file that would produce a hash collision would be malformed and useless.
In general when you hash a message you don't want an attacker to make subtle changes and get the same hash.
"Here is my electronic payment for £100" should never have the same hash as "Here is my electronic payment for £10,000. Nice to meet you on the weekend".