I would like to know if there are any differences in between the two not equal
operators <>
and !=
in Oracle.
Are there cases where they can give different results or different performance?
No there is no difference at all in functionality.
(The same is true for all other DBMS - most of them support both styles):
Here is the current SQL reference: https://docs.oracle.com/database/121/SQLRF/conditions002.htm#CJAGAABC
The SQL standard only defines a single operator for "not equals" and that is <>