Prayer might be seen as living communion with God, while meditation is a reflective or preparatory exercise that may incline one to prayer, yet is not itself the act of addressing the divine. I suspect many sometimes confuse the two, meditating when they think they are praying, and praying when they think they are meditating. That said, I think they are related but much of this will flow from the definitions you hold.

One might ask this: how many who presume to pray are truly opening themselves to God, and how many are merely rehearsing their own desires, making nothing more than a crass shopping list of wants?

Partial disclosure: I have never prayed all that often, and have not mediated in years.

Maybe so, maybe not. Meditation toward God might be indistinguishable from prayer toward God. If not toward God, then toward the ineffable.

Prayer can and maybe should be more than a shopping list of wishes and needs--depending on the religious sophistication of the person praying. "Oh Lord, won't you buy me a Mercedes Benz" is not what I would call a worthy prayer. (Sorry, Ms. Joplin). I'm not Catholic, but I gather that people sometimes say the Rosary in a quite perfunctory manner, though that's only external appearances. The prayer series may help them in a meditative or prayerful way.

Prayer should certainly not be transactional -- "Dear God, IF I do not fornicate with (list names, even though the omnipresent God will be there each time) this week, would you send $3,000 for me to make the overdue mortgage payments?" Does God make deals like Donald? Does God care $3000 whether you fornicate with (list names) or not? Would God be moved by a successful henceforth and forever more vow of chastity? Perhaps your forfeiting the house to the bank is part of God's plan? Maybe He is making arrangements to house a homeless immigrant family? You want to help God, don't you?

Fortunately for our earthly reputations, most of pray silently, so we aren't leaving behind a string of public confessions.

I don't know how many people meditate for "spiritual" purposes. I found mediation most useful for maintaining mental health.

There are monks and nuns who pray for a living. They do pray for specific needs (usually not their own, but on behalf of others) and I gather that they pray toward God.

BTW, from my limited experience I find somebody else's prayers perfectly fine. If the Psalms have been in use for thousands of years, it's because they are effective--for us, especially.

It depends on the perspective. From that of the supplicant, they are entirely different as prayer is a communication with another while meditation is at best a communication with oneself. However from the 3rd person perspective, they are essentially identical.