That distinction doesn't exist in Orthodoxy. Hymnography is just as much prayer as any other act of the Church. We do distinguish between, liturgical, corporate and personal prayer, but all 3 are prayer, and two can't exist without the third.
Our foundation of prayer is the liturgical life of the Church. The services we have where we come together as the whole body (all across the world). This includes litanies (requests, such as "For all those who have gone in this life before us, especially the Priest Miroslav, let us pray to the Lord. Lord Have mercy"), blessings (statements, ie. Blessed is our God, always now and ever, and unto ages), Scriptures (Kathisma's from the Psalms, Epistle and OT readings, as well as the core, the Gospel readings), Hymnography (Troparia and Kontakion for the day, Stichera, for example, Tropar during Pascha is "Christ is Risen from the dead, trampling down death by death, and upon those in the tombs bestowing life"), and every other part of the service. It is all liturgical prayer, and it is our foundation in our prayer life.
The next form of prayer is corporate. This is praying together outside of Church. Whether it be meal prayers together, doing a Trisagion for a loved one, prayers during a meeting or whatever else comes to mind.
Then, the third form is personal prayer. This includes formed prayers, such as evening prayer, morning prayers, prayers for certain needs, as well as informal prayer, and of most importance but most difficult, the prayer of silence ("Be still and know that I am God"). The prayer of silence is more than just silence of the mouth, but silence of the mind as well. There are many writings on acquiring the prayer of silence, many having to focus on the usage of the "Jesus Prayer" ("Lord Jesus Christ, Son of God, have mercy on me the sinner.") to lead into this prayer of silence, but as Elder Cleopa said, it takes years and years to reach the stage of complete silence in prayer.
Lord Jesus Christ, Son of God, have mercy on me the sinner.