Pass the hash starts with a stolen NTLM hash, usually pulled from LSASS memory or the SAM database through credential dumping. The attacker never cracks it to a plaintext password. Instead, a tool like Mimikatz's sekurlsa::pth module injects the hash straight into a new logon session, and Windows accepts it for NTLM authentication exactly as if the password had been typed. The resulting network logon (LogonType 3) carries LogonProcessName NtLmSsp and KeyLength 0, because NTLM authentication never needed a password to derive a session key in the first place.
Overpass the hash and pass the ticket push the same stolen material one step further into Kerberos. sekurlsa::pth can also request a Ticket Granting Ticket using the hash as the secret, producing a real Kerberos ticket (often flagged by an RC4-HMAC encryption downgrade on Event 4768) that the attacker then uses like any legitimate credential. Pass the ticket skips the hash entirely: the attacker steals an already-issued TGT or service ticket straight out of LSASS memory with Mimikatz's kerberos::ptt module and injects it into a different logon session, so the ticket is used from a host it was never issued to.
The cloud and SaaS variant swaps hashes and tickets for session cookies and OAuth tokens. Infostealer malware, adversary-in-the-middle proxies, and browser-session theft lift an already-authenticated token, and because that token represents a completed sign-in (MFA included), replaying it from attacker infrastructure bypasses the second factor entirely. The mechanics differ by platform but the defensive shape is identical across all three: material that should only ever move with its original session shows up authenticating from somewhere else.