Spiritual formation is the continuing response to the reality of God’s grace shaping us into the likeness of Jesus Christ, through the work of the Holy Spirit. This is in a community of faithful, forgiving friends who are on the similar journey - the Church (however it looks). This is a life long journey, a gradual and progressive movement toward spiritual maturity, the image of Jesus, the maturation of love in our lives. These lives of growing intimacy with Jesus will result in healthy, living sacrifices which are witnesses of the Gospel of Love to a hurting world (Acts 1:7-9).
Another term, to describe the process of spiritual formation, is "sanctification." There are three schools of thought with respect to Christian Spiritual Formation. The first holds that the process is that of the Holy Spirit alone without our participation. The second suggests it is us working hard and striving to conform our lives to Christ-like character. While there is some degree of truth in each these position, Christian spiritual formation holds that this is the work of the Holy Spirit in our lives in which we are intentional and full participant realizing, however, at the end of the day, all growth towards maturity is the work of the Holy Spirit (Philippians 2:12-13, Romans 8:13).
It is important to distinguish this from salvation. Salvation is a free gift of God by grace, through Christ. Spiritual formation is not an attempt to "earn" Gods favor, love, acceptance or forgiveness - this was all completed in Christ on the cross. Rather, spiritual formation is the response to God's love, a process where we grow into greater Christ-likeness (Romans 12:2) as the truth and love of God begins to renovate our lives from the heart out (Galatians 5:22-25)! While we never achieve complete sanctification in this life, we grow into maturity (1 Corinthians 14:20, Ephesians 4:12-13, Colossians 1:28, Hebrews 6:1). God is the one, who directs our efforts, not us and the maturing in love (Christ-likeness), is the fruit of a life-long, deepening relationship with God.
Disciple is a word we often see throughout the Gospels and speaks to the individuals who are apprentices of the Master - Jesus. Who are learning to live and serve as Jesus did. While spiritual formation is not specifically mentioned in scripture, its presence is there none the less. Pauls writing is loaded with spiritual formation language and themes like; maturity, growing up into the image of Christ, the fruit of the Spirit, renewing of our minds and many others.
In my opinion, discipleship and spiritual formation are not really synonymous. Discipleship is the means of spiritual formation. It is the lifelong work of transformation of our entire being. Contrary to the self-help industry which will focus on one aspect of who we are, spiritual formation focuses on the whole person, and more specifically a healthy foundation upon which everything else (literally EVERYTHING else) will be built. Upon a firm foundation, a building can be built which will withstand the storms of real life in the real world. Spiritual formation entails the transformation of mind, body, emotions, thoughts, and social relations – the stuff character is made of. Transformation implies action and, “ … character is formed through action and transformed by action."* Discipleship and the process of spiritual formation is more than the acquiring of information but the integration of that information as a part of a healthy faith in all of life in the context of personal relationship with God. The difference being - knowing God versus just knowing about God.
* Willard, Dallas. The Great Omission; Reclaiming Jesus’s Essential Teaching on Discipleship Harper San Francisco. 2006 pg. 65