At a fairly basic level, Mormons and Episcopalians don't define prayer in the same way. Here is an except on prayer from the LDS Bible Dictionary:
.... As soon as we learn the true relationship in which we stand toward God (namely, God is our Father, and we are His children), then at once prayer becomes natural and instinctive on our part (Matt. 7:7–11). Many of the so-called difficulties about prayer arise from forgetting this relationship. Prayer is the act by which the will of the Father and the will of the child are brought into correspondence with each other. The object of prayer is not to change the will of God but to secure for ourselves and for others blessings that God is already willing to grant but that are made conditional on our asking for them. Blessings require some work or effort on our part before we can obtain them. Prayer is a form of work and is an appointed means for obtaining the highest of all blessings....If, as in the Mormon perspective, prayer is supposed to be a conversation between a literal Father (in heaven) and a child (on earth) to bring their minds together so that the child knows what to ask for to be able to get what the father really wants to give, why would you use predetermined phrases out of a book? It would be like trying to ask your parents for a birthday present by reading quotes out of Shakespeare. Except in special circumstances it simply wouldn't make sense.
We pray in Christ’s name when our mind is the mind of Christ, and our wishes the wishes of Christ—when His words abide in us (John 15:7). We then ask for things it is possible for God to grant. Many prayers remain unanswered because they are not in Christ’s name at all; they in no way represent His mind but spring out of the selfishness of man’s heart.
For contrast, here is a description of prayer from the Catechism in the Book of Common Prayer:
Q. What is prayer?
A. Prayer is responding to God, by thought and by deeds, with or without words.
Q. What is Christian Prayer?
A. Christian prayer is response to God the Father, through Jesus Christ, in the power of the Holy Spirit.
Q. What prayer did Christ teach us?
A. Our Lord gave us the example of prayer knows as the Lord's Prayer. See page 364.
Q. What are the principal kinds of prayer?
A. The principal kinds of prayer are adoration, praise, thanksgiving, penitence, oblation, intercession, and petition.
Q. What is adoration?
A. Adoration is the lifting up of the heart and mind to God, asking nothing but to enjoy God's presence.
Q. Why do we praise God?
A. We praise God, not to obtain anything, but because God's Being draws praise from us.
Q. For what do we offer thanksgiving?
A. Thanksgiving is offered to God for all the blessings of this life, for our redemption, and for whatever draws us closer to God.
Q. What is penitence?
A. In penitence, we confess our sins and make restitution where possible, with the intention to amend our lives.
Q. What is prayer of oblation?
A. Oblation is an offering of ourselves, our lives and labors, in union with Christ, for the purposes of God.
Q. What are intercession and petition?Obviously intercession and petition are very similar to the Mormon definition of prayer, but that that is only one portion in a much larger picture. Obviously a definition is only a definition and in real life most all Mormons do more in their prayers than just ask for things. However, I believe the emphasis in the definitions represents a real cultural difference. Contrasting with this idea of prayer being a form of work used to earn conditional blessings, Episcopal Priest Christopher Weber in his book "A Users Guide to Morning and Evening Prayer" describes prayers known as the Daily Office as follows:
A. Intercession brings before God the needs of others; in petition, we present our own needs, that God's will may be done.
...we are sanctifying time by framing each day with prayer. No matter the setting, the goal of the Daily Office remains the same: to provide opportunity for every Christian to offer each day to God.In some respects the daily prayers of a Mormon and an Episcopalian have similar roots, both going back in some sense to ancient Jewish rituals of regularly praying at different times of the day. These traditions were in new forms passed into Christianity where they later became highly developed in the prayers of monks and nuns. During the Reformation when monasteries were dissolved, the English church adapted these prayer rituals for use by every day people. The Episcopal church, like many others, carries on a beautiful version of this tradition. For an example of the beautiful prayers that can be found in these services, consider the following from an Evening prayer:
Keep watch, dear Lord, with those who work, or watch, or weep this night, and give your angels charge over those who sleep. Tend the sick, Lord Christ; give rest to the weary, bless the dying, soothe the suffering, pity the afflicted, shield the joyous; and all for your love's sake. Amen.or another example from evening prayer:
O gracious light,While this prayer is not asking for anything it works beautifully to sanctify the day. This particular prayer is often set to music.
pure brightness of the everliving Father in heaven,
O Jesus Christ, holy and blessed!
Now as we come to the setting of the sun,
and our eyes behold the vesper light,
we sing your praises, O God: Father, Son, and Holy Spirit.
You are worthy at all times to be praised by happy voices,
O Son of God, O Giver of Life,
and to be glorified through all the worlds.
Another form of prayer that I am fond of is the Christian meditation practice known as Centering Prayer. The deep sense of calm I gain from this practice makes it one of the spiritual highlights of my day. Of all the kinds of prayer I now enjoy, it is probably the farthest from the Mormon experience because it isn't focused on trying to speak with or for God. Instead it is resting one's mind in God. What is that like? This video provides some perspective.
I still at times practice prayer as conversational requests, but only as one dish in a much larger spiritual feast. My prayer life has changed so much I'm not even sure my coworkers can tell I am praying when I make my morning and noon prayers. Instead of the typical Mormon posture of bowed head and closed eyes I perform these prayers consulting either a physical or electronic copy of "The Book of Common Prayer." Instead of taking care to be inventive in how I phrase of my daily requests to avoid meaningless repetition I worry whether I am pondering the my words sufficiently to recite them with full intent of heart. Instead of worship through moving my body only happening in temple ordinances I worship that way regularly. Prayer can be many more things than it used to be. Instead of judgement regarding whose prayers are best, I wish the Mormonism I grew up in had been more open to exploring the diversity of spiritual practices in the world. I am not sure how this would have been possible. Most of the cycle worship I practice now would need some modification to work for Mormonism, though not very much. The one piece I very much wish was shared more broadly is Centering Prayer. While the chief proponent of Centering Prayer is a Catholic monk the practice and generally the theology of centering prayer is non denominational. There is no good reason that I can see why Mormons could not participate in the Christian meditation tradition. If I could give a gift to the prayer life of the Mormons that I know, that would be it.