What's the difference exactly because I don't really see any here since either way moderators are the ones executing the ban or is the reason for the ban what classifies it as either autoban or Nuke user. From what LoyceV said nuking seems to be an entire deletion of the account.
Let me quote two explanations for you
First is Theymos which says it’s just a name
I only changed the message on autobans. ("Autoban" = lingo indicating a type of ban. They're usually not actually automatic.)
And the a broader explanation by BadBear
There are 2 types of bans.
Autobans. Isn't what it sounds like, it means someone pressed the ban button, but it's automatically carried out, as opposed to be manually entered. Though there is a mod or two running scripts because of the spammers. This results in the message You were banned by a forum moderator, email xxx. Both global mods and admins use this, so it isn't a guarantee it was a moderator, just more likely. I use autoban instead of manual bans for permanent bans because it's faster and more efficient. All bans in the modlog are autobans, and permanent.
Autobans ban the account involved only, you can still log in and do everything normally, just can't post or pm. It also adds units of evil to the IPs used, a new account created using these IPs will need to pay a fee. Units of evil increase with additional bans. Nuking is essentially an autoban+deletion of posts.
Manual bans are only available to admins, and are generally configured the same way as above, though it's possible to increase the scope of the ban to include things like registering from certain emails/providers, ips, subnets, hostnames, etc. Can also add multiple accounts to the same ban. It's also possible to prevent banned users from logging in at all using the banned account, this will prevent them from being able to read the forum and access pm's too though, so I rarely use it. These result in the customized reason for the ban+duration, insubstantial posts or whatever.
Then as for Nuke user it’s simply a ban to newbies with less activity than 30 and when banned all post are deleted. This is much that I know, both Auto ban user and nuke user the same but deletion of posts is the major difference.
Then under this bans we have
Permanent ban
Temporary ban
Signature ban