SASL and gssapi basically solve the same problem in different ways. Both ways are to find the best common authentication method to use between the two systems.
No, gssapi is not used under the hood in SASL unless you use something like RFC4752
Yes, you can use gssapi without SASL, examples of this would be a typical entry in a Linux machine in a Windows AD domain through the kerberos / gssapi providers.
It all depends on which authentication scenarios you should implement, and both SASL and gssapi use them. GSSAPI is most often used with the Kerberos system.
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