You can always connect to DB either ways.
When you are connecting to DB using db links it will use Global DB name if you have Global Names value is set to true. You have to use the same global name to connect.
Instance is set of backgroung processes you create on the database . You can have more than one instance on one database.
You can always rename the global name .
alter DB rename global_name to ' ';
The SID is a unique identifier that you can use to refer to an instance of
the database that is available on your system. Use the SID field to specify a
unique identifer for the default instance that will correspond to the starter
database -- "oracle" is a common choice.
A database global name is the complete name of the database, including the
database's encompassing network domain. The database's global database name
has a format of db_name.domain_name. The db_name portion of the global name
must be 8 characters or less and consist of alphanumeric characters, and it can
contain special characters _, #, and $. The domain_name portion of a global
database name must be 128 characters or less. (ie. oracle.animatedlearning.
com -- default SID is oracle & domain is animatedlearning.com).