Both Distinct Honor and Privilege are used when talking about something that is of special value or advantage to experience or have.
Distinct means specific, unquestionable, easily seen to be different from other things.
“Garlic has a distinct smell.”
This means that the smell is clearly specific to garlic and smells different to other things.
Honor means different things. Firstly, honor can mean something of high respect. Or, it can mean that it is of great benefit or a symbol of respect.
“It’s an honor to be here”.
This means it is a sign of great respect and good fortune (to feel lucky) to be there.
A Distinct Honor is a stronger ways of saying honor and means to be specifically respected. It’s a polite term used in formal situations.
For example “It’s a distinct honor to meet the Queen of England”.
This means it is an enormous sign of respect and good fortune to have the chance to meet a person like Queen.
Privilege is a special advantage or a benefit received. It is more connected to something earned or that the person has worked for.
For example “Expensive champagne is a privilege of flying first class.”
You would not say it is an honor to receive the champagne. Because it is part of the benefit of a first-class ticket purchase. It’s not a symbol of respect.