The difference and connection between the role dbo sysadmin public

DBO: is a user with implied permissions to perform all activities in the database.

Sysadmin:sysadmin fixed server role

Any member of the sysadmin is mapped to a special user within each database called dbo
Any object created by any member of the sysadmin automatically belongs to the DBO

Public: is a special database role that is owned by each database user.
Captures all default permissions for users in the database.
Users, groups, or roles cannot be assigned to it because they belong to that role by default.
Included in each database, including master,msdb,tempdb,model , and all user databases.
cannot be dropped.