As I understand it,
Am I completely lost?
Trying to figure out how it works but information, is either too precise or not enough.
Not quite.
SPN simply means 'Server Principal Name' and is the AD or Kerberos slang for the service you try to authenticate against.
Kerberos is a user authentication service, more or less yes. It also provides security for network messages and calls between services.
SPNEGO-GSSAPI* is a kind of strange beast. GSSAPI (Generic Security Service Application Program Interface) is an API to (in principle) different authentication services, it provides negotiation of the mechanisms used. Often the only mechanism available will be Kerberos though. It is the usual API to attach 3rd party programs to Kerberos when you are on Unix (defined in various RFCs, for example RFC 2743 )
On the windows platform SSPI is the generic layer, so it compares to GSSAPI.
SPNEGO is kind of a strange hybrid. It is a mechanism to be used in SSPI, HTTP Auth or GSSAPI which negotiates another auth protocol (for example Kerberos or NTLM if you are on Windows), so it basically does the same thing GSSAPI does again in a different way.
Typical uses of SPNEGO are HTTP authentication to a windows domain, for example IIS uses it if you use 'Integrated windows authentication'. It is also used when you select the 'Negotiate' options for SSPI. See for example RFC 4559
Almost all of your understandings are wrong.
Here it goes:
