1, The full form of Conf is Conference. It’s used on Associations & Organizations ,Conferences & Events in Worldwide

Conference (Conf.) is a formal event for the exchange of information or discussion, typically one that takes place over several days.

• a meeting for consultation or discussion:

a conference between a student and his adviser.

• the act of conferring or consulting together; consultation, especially on an important or serious matter.
• Government. a meeting, as of various committees, to settle disagreements between the two branches of the legislature.
• an association of athletic teams; league:an intercollegiate conference.
• Ecclesiastical.
  1. an official assembly of clergy or of clergy and laity, customary in many Christian denominations.
  2. a group of churches whose representatives regularly meet in such an assembly.

2, The full form of Conf is Confidential. It’s used on Governmental ,Military in Worldwide

Confidential (Conf.) means secret or private.

Confidentiality involves a set of rules or a promise usually executed through confidentiality agreements that limits access or places restrictions on certain types of information.