This episode provides the answer to the question, demonstrating that Paul's omission of the word "saints" in his intro to the Galatians is best explained by analyzing Paul's letters chronologically. The earliest letters Galatians (49) and 1 and 2 Thessalonians (50 and 51) omit the "word" saints in the intro, though the Thessalonian correspondence uses it in the body of the letters. Paul directed these 3 letters to "churches." 1 and 2 Corinthians, written next (55 and 56), are addressed both to "churches" and "saints." The last 4 letters (Ephesians, Philippians, Colossians, and Romans, written 57-62) are not addressed to churches at all, but just to saints. The best explanation of the omission of the word "saints" in Galatians is therefore stylistic: the omission is consistent with the omissions to the Thessalonians written at the same time and Paul's last 4 letters don't use the word "church" at all in the intro. Paul nevertheless considered the gatherings of saints as "churches," though he chose not to specifically address "churches" in the intro.
“Also no Salutations to Saints in Thessalonica”
On the road to answering the question regarding the omission of the word "saints" in the intro to Galatians, this episode notes that the same omission occurs in the books of 1 and 2 Thessalonians. Paul uses the words "saints" in 6 of his 9 epistles to churches. The episode notes Augustine's distinction between the visible and invisible church, and posits that Paul addressed his letters to the visible church, which included believers and unbelievers. Christ's use of the word church in Matthew 16:18 only referred to believers. "Upon this rock, I build my church." The distinction between the visible and invisible church might possibly influence how the question is ultimately answered.
The Grounds of “Sainthood”
This initial episode lays the foundation needed to properly answer the question concerning Paul's omission of the word "saints" in his salutations to the Galatians. Most of Paul's letters to churches are addressed to saints, even 1 Corinthians, a very carnal church. The ground of "sainthood" in Paul's theology is the imputed righteousness of Christ, the gift of Christ's perfect holiness that is accounted to everyone who embraces Christ. The Christian's fundamental identity is his POSITIONAL holiness before a holy God, who regards us through the blood of Christ, and ACCOUNTS us holy. Christ's gift of His righteousness to believers is therefore the ground of "sainthood." Another meaning of "hagios" [saint in Greek] is "consecrated" or "set aside," both of which indicate the calling dimension of sainthood. the church is literally composed of those who are "called out," the literal meaning of church. "ekklesia" Consequently Paul describes believers in Corinth as "those who have been sanctified in Christ Jesus, saints by calling." (1 Cor. 1:2) "Sanctified" here is derived from the same root as saint. Saints then are those called and set aside by God to receive Christ's positional holiness. This foundational plank of the Christian faith, our sainthood in Christ, is the basis for all subsequent growth in practical holiness, in which the Holy Spirit conforms our sinful CONDITION to our perfect POSITION in Christ.