Philippians begins like other letters in Paul's day. Paul gives his name and that of Timothy. Paul is not only a Roman Citizen, he is also a Christian. Paul always wrote with the intent of presenting the Gospel and dealing with people.
Paul is writing this letter as a slave to saints. The word saints appears in regards to believers over 60 times whereas the word Christian only appears three times.
Saints, in Scripture, is a term used for those who are sanctified in the Lord Jesus. Those who are separated from the world are Saints. We, as God's people are Saints. Redeemed people are now Saints and we are called to serve Him.