How is prayer different in Buddhism when compared to theistic religions? We all know the concept of kamma-vipaka and that we should strive and create the causes of our happiness.

I understand the Buddhas only point the way, they teach the Dhamma and we are responsible for walking the path. In this context, why it is so commom for Buddhists to pray? For example, does prayer in Buddhism have a different meaning when compared to for example Christianity?

I can understand why praying is so important in religions with a creator God, because that is the way you ask for all sorts of blessings, but in Buddhism it is not so clear, does praying have a different meaning or purpose?
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.