What's with all the "name"s-short, long, user, computer?

I'm a long time Mac user but not lots of experience with multiple user accounts.

Trying to migrate from MB with one account to MBA; on about the 7th or 10th erase & install. Various methods of getting the data over are not working.

I'd like to have a new "home" account name, but the more I read the more confused I'm getting-there are so many different "name"s in the sharing/accounts windows I'm not sure if they are variations of each other or all different. Is there a table somewhere that tells the meaning of/difference among
short name
long name
home folder name
computer name
user name
account name
etc?

Apparently I can't migrate MB=MBA into a new short name, so have to do some trickery with advanced settings, or migrate then make a new account, drag/copy/from then delete the old account. What junk!

You'd a thunk Apple would know people would want to migrate a home folder to new machine and change the name of it along the way.

Phew. Not impressed so far with the ease of transition to MBA. 3 days in the works now.