My view on the differences between prayer and meditation were mentioned elsewhere, so I thought I'd offer the following. As a general discussion, I've chosen my terms of reference from the Sophia Perennis.
On prayer, I'd reference Frithjof Schuon:
The remembrance of God is at the same time a forgetting of oneself; conversely, the ego is a kind of crystallization of forgetfulness of God. The brain is, as it were, the organ of this forgetfulness; it is like a sponge filled with images of this world of dispersion and of heaviness, filled too with the tendencies of the ego towards both dispersal and hardening. As for the heart, it is the latent remembrance of God, hidden deep down in our “I”; prayer is as if the heart, risen to the surface, came to take the place of the brain which then sleeps with a holy slumber; this slumber unites and soothes, and its most elementary trace in the soul is peace. “I sleep, but my heart waketh.” (Understanding Islam)
The aim of individual prayer is ... the purification of the soul: it loosens psychological knots or, in other words, dissolves subconscious coagulations and drains away many a secret poison; it externalizes before God the difficulties, failures and tensions of the soul, which presupposes that the soul be humble and upright; this externalization – carried out in face of the Absolute – has the virtue of reestablishing equilibrium and restoring peace, in a word, of opening us to grace. (Echoes of Perennial Wisdom. It should be noted that the Sacrament of Confession or Reconciliation, is precisely this same process in concrete form)
The important thing to grasp here is that actualisation of the consciousness of the Absolute, namely the “remembrance of God” or “prayer,” insofar as it brings about a fundamental confrontation of creature and Creator, anticipates every station on the two axes. It is already a death and a meeting with God and it places us already in Eternity; it is already something of Paradise and even, in its mysterious and “uncreated” quintessence, something of God. Quintessential prayer brings about an escape from the world and from life, and thereby confers a new and Divine sap upon the veil of appearances and the current of forms, and a fresh meaning to our presence amid the play of phenomena.
Whatever is not here is nowhere, and whatever is not now will never be. As is this moment in which I am free to choose God, so will be death, Judgment and Eternity. Likewise in this center, this Divine point which I am free to choose in the face of this boundless and multiple world, I am already in invisible Reality. (Logic and Transcendence)
On meditation:
The contact between man and God here becomes contact between the intelligence and Truth, or relative truths contemplated in view of the Absolute ... Meditation acts on the one hand upon the intelligence, in which it awakens certain consubstantial “memories,” and on the other hand upon the subconscious imagination which ends by incorporating in itself the truths meditated upon, resulting in a fundamental and as it were organic process of persuasion ...
Meditation – as defined in the language of the Vedanta – is essentially “investigation” (vichara) leading to the assimilation of theoretical truth, and then discernment (viveka) between the Real and the unreal. (Stations of Wisdom)
This latter pinpoints the axiom of all prayer and meditation, 'the discernment between the Real and the illusory', petition in prayer, and discipline in meditation, is then cleaving to the Real.
Contrary to what is too often stated, meditation cannot of itself provoke illumination; rather, its object is negative in the sense that it has to remove inner obstacles that stand in the way, not of a new, but of a pre-existent and “innate” knowledge of which it has to become aware. Thus meditation may be compared not so much to a light kindled in a dark room, as to an opening made in the wall of that room to allow the light to enter – a
light which preexists outside and is in no way produced by the action of piercing the wall ... The role of meditation is thus to open the soul, firstly to the grace which separates it from the world, secondly to that which brings it nearer to God and thirdly to that which, so to speak, reintegrates it into God. (The Eye of the Heart)
Meditation / Concentration / Prayer: These three words epitomize the spiritual life, while at the same time indicating its principal modes. Meditation, from our standpoint, is
an activity of the intelligence in view of understanding universal truths; concentration, for its part, is an activity of the will in view of assimilating these truths or realities existentially, as it were; and prayer in its turn is an activity of the soul directed towards God. (To Have A Center)
So, from the last, meditation is mind training. It's the necessary practice of self-discipline as a means of approach, but it is not, in itself, the means of enlightenment. The goal is defined by the tradition, and this shapes the meditative practice.
The spiritual benefits of meditation are generally over-blown. Meditation tends to be regarded as the be-all in Buddhism, but that I think is a misunderstanding. In the Christian Tradition, meditation is a step along the way of prayer.
In modern parlance, the higher prayer is 'quality time' between creature and Creator, or 'active listening', that is, between I and Thou, to the exclusion of all else.
