Is there more than one "process" to generate the hash and why can it be different?
There is only one process to generate a hash, however there are many ways to generate an address.
I understand and I consider the hash of the address number 1 as "main"
I ask, because I am considering using Altcrack
Assuming you are not one of those guys wasting your time checking all private keys, when you want to "recover" something you should already have your address or at the very least have an idea about its type. For example an old wallet created in 2016 would be P2PKH using compressed public key.