How is prayer different in Buddhism when compared to theistic religions?

Whether "it is so common for Buddhists to pray" is unclear as there does not appear to be non-subjective evidence to support that claim. It could be said that the emphasis given to prayer in theistic religions is generally given to meditation in Buddhism. Some forms of meditation, such as metta (sending thoughts of universal friendliness) have a prayer like quality to them. But surely some Buddhists do pray and to whom these prayers are sent is spoken about in the book "The Energy of Prayer" by Thich Nhat Hanh, a Buddhist monk and prolific author.

"But when we recite these lines, we are not just handing this desire over to the Buddha. We are gathering our strength from within and combining it with the strength that lies outside us."

Another quote from this book is

"the one who prays and the one prayed to are two realities that cannot be separated from each other. This is basic in Buddhism, and I'm quite sure in every religion there are those who have practiced for a long time and have this understanding. They can see that God is in our heart. God is us and we are God."

So that is one interpretation from zen master Thich Nhat Hanh.

Does praying in Buddhism have a different meaning or purpose as compared with religions with a creator God?

There are various points of view, depending substantially on the intent or state of mind of the person praying. I'll give you three of those points of view (POVs)

From the POV of the typical Christian, it absolutely has a different meaning. For example, in Catholic Christianity, prayer is "the uplifting of the heart and mind to God" (from the Catechism). Prayers are typically done to, through and "in the name of" Jesus, one of the three "persons" in the single tri-une God. God -- the personal, omnipresent, omniscient, omnipotent, omnibenevolent creator of everything -- is front and center of Christian prayer. If God is not front and center then best case it's not prayer, and worst case it may even be seen as downright dangerous and at risk from the influence of evil spirits. The primary purpose of Christian prayer is to bring the creature into union with the Creator (worship, praise, and also intercession are all components in that).

From the POV of the typical praying Buddhist, there is no such "fully featured" God, so again the meaning is clearly different. A common purpose is, as with meditation (which is very like, although not identical to, some contemplative forms of prayer), to help train the mind as part of the path to enlightenment.

However, finally, from my POV, I think it is hard to overlook the marked similarities between Christian prayer and Buddhist prayer and meditation, if you see past the difference created by the (excessive) anthropomorphizing of the concept of God. For example, the first time I participated in a chanting session in a Zen center, I was struck by how similar it felt to the many times in my childhood when I attended a Catholic Rosary service. Many Catholics, especially post Vatican 2, have tried to stress the importance of saying prayers in one's own language and in understanding and meaning the actual words. But via Zen, I came to see the value in the almost mantra-like quality of the high-speed Rosary, and of prayers and hymns in languages other than my own. This Latin, for example, is beautiful to my ears, and spiritually uplifting: https://www.youtube.com/watch?v=yYxyiUB1L0s

For another example, look at this extract from the Eighth Letter in the 17th Century "The Practice of the Presence of God" by Brother Lawrence of the Resurrection:

"...concentrate on keeping your mind in the presence of the Lord; if it sometimes wanders and withdraws itself from Him, do not let it upset you; confusion serves rather to distract the mind than to recollect it; the will must bring it back calmly; if you persevere in this way, God will have pity on you."

To me that bears a striking resemblance to instructions for Buddhist meditation. The main difference -- the idea of God -- is a difference only if, as I say, you take very literally the typical anthropomorphic view of "God". But if you see past that -- and surely whatever God is, if indeed God "is", then "he" is certainly not an old white dude with a long beard sitting up in the clouds -- my view is that there is often actually very little difference between Buddhist prayer and Christian prayer. This is, of course, a minority view! (Which doesn't, on the other hand, make it wrong.)

In short, most Buddhisms are not devotional and their religious recitations (prayers-- a very Christian work) are not devotional. Old school lay Buddhism in many places is very devotional, monastic Buddhism is less so, modern western secular Buddhism isn't devotional at all.

Not speaking of Pure Land (someone else should address that because I suspect it would have interesting similarities to theistic prayer), there are many things that Buddhist say that are not of the same sort as theistic prayer, but could be depending on how it's worded.

Repentance. Repentence is saying what you did wrong and promising to stop doing wrong. Said that way, it's not a prayer. If it involves getting a supernatural being to purify you of your bad Karma, then it's prayer.

Meal Gatha. A meal gatha (a gatha is a verse), is all about reminding you who brought the food to the table (workers and donors) and how you ought to be practicing hard to be worth it. If you are saying thanks to supernatural beings for providing your food, then it's theistic prayer.

Manra. In the Indian world, there was a belief that the spoken world created reality. This evolved into mantras. So mantras essentially work like Harry Potter magic. Who cares, for the moment, if mantras work. They work by ones own power. Unless they are like Nembutsu, which every explicitly works via other power (Amida's grace)

Dedication of Merit. This is just disavowing credit for your own good deeds and possibly magically transferring your good karma credits to others.

Vows. These are often heroic goals that you plan to implement yourself. Some of the vows are made by Buddhas and Boddisattvas, vowing to take care of other people-- get them to a Pure Land, make them healthy again and so on. I think if people just read the vows and wait for the celestial Buddha's to deliver on their promises, that's devotion. If you read or recite the Medicine Buddha's vows and think that these are good vows that everyone should make, then that's not so devotional.

Praise. There is a lot of praise going on in Mahayana texts. If it is reminding people of what the goal is, namely to some day, some kalpa to become a Buddha, then it serves the purpose of focusing your attention on the goal and the merits. If the praise is a quid pro quo to get the celestial beings to reward you, help you and so on, it's devotional.

I am a practicing Buddhist in Theravada tradition from Burma(Myanmar), as far as I know the praying in Buddhism can be either one of the 2 things.

1. Reciting the tachnings of Buddha or others great teachers in tradition probably to remind oneself of tachings and for tranqulity of mind

2. Actully asking for some blessing but not from Buddha but from benovelent dieities (who may or may not help) in witness to your merit or virtue

Hope that help

Why is it so common for Buddhists to pray?

Generally speaking, before going into the specifics of Buddhist practice, people pray because they are looking for a support, because they want to be happy and free from suffering; they pray when things are out of their control, in order to help bring about desired results. Ordinary Buddhists are just people looking for a good future.

As in all things, one can't judge a religion by what is "common" among its followers; it stands to reason that the majority of practitioners in any religion will not be serious about their religion and practice it only insofar as it supports their worldly pursuits. Hence the popularity of prayer over say meditation.

The Buddha's attitude towards theistic supplication is well-summarized in the Jaataka commentary:

These greedy liars propagate deceit,
And fools believe the fictions they repeat;

He who has eyes can see the sickening sight;
Why does not God set his creatures right?

If his wide power no limits can restrain,
Why is his hand so rarely spread to bless?

Why are his creatures all condemned to pain?
Why does he not to all give happiness?

Why do fraud, lies, and ignorance prevail?
Why triumphs falsehood,—truth and justice fail?

I count your God one th’ injust among,
Who made a world in which to shelter wrong.

Jāt. 543

He also implicitly pokes fun at the concept of supplication in the Ratana Sutta, acknowledging the prevalence of prayer and encouraging higher beings to respond positively:

O beings, listen closely. May you all radiate loving-kindness to those human beings who, by day and night, bring offerings to you. Wherefore, protect them with diligence.

http://www.accesstoinsight.org/tipitaka/kn/snp/snp.2.01.piya.html

Does prayer in Buddhism have a different meaning when compared to for example Christianity?

In Theravada Buddhism, the word used is adhiṭṭhāna, which means "determination" or "resolution", in the sense of setting one's mind (ṭhāna) firmly (adhi) on something, e.g. "May I be free from suffering". Though the translation makes it sound like a request, it is actually just a means of reaffirming one's commitment to something - one's own happiness, the happiness of others, the attainment of enlightenment, etc.

An example of a core Buddhist determination, one made by the Buddha himself, is:

‘Willingly, let only my skin, sinews, and bones remain, and let the flesh and blood dry up on my body, but my energy shall not be relaxed so long as I have not attained what can be attained by manly strength, manly energy, and manly persistence.’

MN 70 (Bodhi, trans.)

In other Buddhist traditions, prayer may actually be used as a means of supplication, e.g. to a bodhisatta or even a presumed Buddha.